Asked by Brad Peterson, student, Roy High on January 29, 1997: I was watching an episode of The Simpsons the other day, the one where Homer gets sucked into the third dimension, and in this 3-D world, there was an equation that said . Also, the min supremacy time is a forgotten bit at the end from an earlier strategy. Since the 1.4 update, a third minigame has shown up, Arrow. It only requires a pump discharge pressure of 68 psi to flow a 150’ attack line with an 1 3/16” tip flowing right at 5 gallons per second. By using this website, you agree to our Cookie Policy. Show working. Edited for errors overlooked in the original post. The exponential function also has analogues for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra. The formula is used where there is continuous growth in a particular variable such population growth, bacteria growth, if the quantity or can variable grows by a fixed percentage then the exponential formula can come in handy to be used in statistics Let us calculate a 15 day EMA considering Day 1 as the oldest and D15 as the latest value. . Why 3 seconds ? x(t) = x 0 × (1 + r) t. x(t) is the value at time t. x 0 is the initial value at time t=0. Show result in exponential format. Been on that one for a while and progress was super slow, so i just used some simple check for upgrade costs, but without your idea of checking the max time for prestige and min time for supremacy. I dont think it does anything. I'm trying this out, happened on this post 3 minutes after you posted :). f (t + dt) = f (t) × ebxdt Exponential Idle is a math-inspired incremental game. I have seen this operating pressure to be nearly idle for many modern fire pumps. Exponential growth/decay formula. Imagine if you set up a preconnected 5 gallon per second attack line to the point that it could be supported at idle. Rule of thumb: To idle a pump when it is unloaded will require about 5% of its full rated horsepower. it describes the inter-arrival times in a Poisson process.It is the continuous counterpart to the geometric distribution, and it too is memoryless.. Why divide by a duration ? Change when better is found. I hope this is the largest addendum I do, given that this section is looking longer than the entire rest of the post. To do so, you have to step through time by tapping the equation or simply let the time follow its course. Won't this just activate whenever the next psi upgrade is available? Euler's formula relates its values at purely imaginary arguments to trigonometric functions. In mathematics, the Chebyshev function is either of two related functions. Achievement Name Task Hint Stars Notes 1 Welcome To The Dark Side: Use the dark theme. We will also discuss what many people consider to be the exponential function, f(x) = e^x. Provides a lower or higher volume line selection option with the fog at a mid range pressure. Inches of Water. There is the 15-Puzzle, a sliding puzzle, and Torus Puzzle (inspired by Loopover and RotSquare), a 2D version of the Rubik's Cube. Free exponential equation calculator - solve exponential equations step-by-step This website uses cookies to ensure you get the best experience. What stage of the game are you in? New comments cannot be posted and votes cannot be cast, More posts from the ExponentialIdle community, Subreddit for the idle/incremental game Exponential Idle, Press J to jump to the feed. Since st is increasing, d(ln(dpsi/(psi+1)+1)/st) will always be negative right after a prestige. Currently I use [((db/b > 1e6 && costUpP(1) < mu + dmu) || (db/b > 1e6 && costUpP(2) < mu + dmu) || (db/b > 1e7)) && pt > 300]. Clearly, the points do not lie on a straight line, so we reject a linear model. 30 minutes feels way too fast. Hey That's interesting one Could you explain me existence of ...<0>3 Wouldn't that be an infinite loop since 0 never will be bigger than 3? 2) derived from the power series of the exponential map of a linear endomorphism, as in matrix exponentiation. I cant keep up with all the content over there. Instead of a single formula, there are several candidates that all need testing. Your goal is to stack up money by taking advantage of exponential growth. Why is e^(pi i) = -1? (in psi or other pressure units) Patm Standard atmospheric pressure (in psi or other pressure units) All three pressure units must be the same. Kongregate free online game True Exponential - The first idle/incremental game featuring exponential progress! Press question mark to learn the rest of the keyboard shortcuts. To help streamline a bit, I also made them all fit my own standardized prefix. We use cookies on our websites for a number of purposes, including analytics and performance, functionality and advertising. If we draw a line between … EDIT: I performed another supremacy and my y exponent has gone up to 3.4 and I've unlocked x4, Well I read it and I think I found a problem with yours (and I think it is unnecessary complicated) Thing is that your dB/b factor is static If u set it up to be d(dB) < dB/(some number) it basically will perform prestige action only when your db will start to slow down And u can Control the lowest growth speed before prestige by deviding it by bigger number. Dangit, you're right. Remember that our original exponential formula is equal to y = ab x.You will notice that in the new growth and decay functions, the value of b (that is growth factor) has been replaced either by (1 + r) or by (1 - r). I'm still at lower levels (5000ish) but it seems to work fine, definitely better than the "discord" expression. In this article, we will discuss what is exponential distribution, its formula, mean, variance, memoryless property of exponential distribution, and solved examples. In Exponential Growth, the quantity increases very slowly at first, and then rapidly. Okay, this took all day of my intermittent Exponential Idle efforts. The formula to define the exponential growth is: y = a ( 1+ r ) x. Tl;dr: Test different supremacy formulas. Edit: Also I made 200k supremacy points in 1h using this (X1), I use: timer(d(ln(1+db/b)/pt)<0)>3 && db/b>2, Its quite slow to accure anything from f(x), but then again im currently sitting at ee2400+, Im sitting round waiting for the next update or a new optimized equation that works better to appear, Hi currently sitting at ee2400+, I'm Dad. Why is e^(pi i) = -1? Ask a question or add answers, watch video tutorials & submit own opinion about this game/app. Free logarithmic equation calculator - solve logarithmic equations step-by-step ): We use cookies on our websites for a number of purposes, including analytics and performance, functionality and advertising. Exponential Growth/Decay Calculator. Are you testing against the speed of increase ? Exponential Growth. 1 2 Wrong Ratio: Try to input an invalid auto prestige ratio. Edit: updated formula(s) at end of post. Solution: First, we calculated the Moving average of three days. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Works fine enough. In mathematics, the gamma function (represented by or Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers.The gamma function is defined for all complex numbers except the non-positive integers. More posts from the ExponentialIdle community, Subreddit for the idle/incremental game Exponential Idle, Press J to jump to the feed. Let us understand this concept by looking at a simple example. The exponential function is a special type where the input variable works as the exponent. 4 Can you add 'insert name here' as a minigame? 1 inch of water is the pressure exerted by a 1 inch high column of water at a given temperature . It is used everywhere, if we talk about the C programming language then the exponential function is defined as the e raised to the power x. 75 psi Fixed gallonage fog at 150 GPM with a friction loss of 25 psi per 10 0’(2) = 125 psi pump discharge pressure matched with 50 psi 15/16” smooth bore at 185 GPM with a friction loss of 40 psi per 100’(2) = 130 psi pump discharge pressure. The second Chebyshev function ψ(x) is defined similarly, with the sum extending over all prime powers not exceeding x Your goal is to stack up money by taking advantage of exponential growth. For LR leak rate (in scc/m), the formula above is converted to: V x (dPmeas – dPno-leak) x 60 sec/min Derivatives and differential equations Should specify the first two psi upgrade types. Provides a lower or higher volume line selection option with the fog at a mid range pressure. I changed the "end of prestige" clause to a "beginning of prestige" clause without thinking. Exponential Distribution Formula. Minigames are one of the various ways to gain additional stars and achievements. To do so, you have … 2 What is the optimal Auto Prestige db/b ratio? f (t+dt) = f (t) * e^ ((b*x*dt)^a), where a = 1/ (1+e^ (-pt/50)) and pt is the time since last prestige in seconds. Exponential Smoothing One of these is called “exponential smoothing.” it works like this: Let X(N,1) be the 1st prediction based on a series of length N. In general X(N,q) is the qth prediction after the last in the time series. d(db) < 0.2 && min( costUpP(1), costUpP(2) ) < mu + dmu ). Free exponential equation calculator - solve exponential equations step-by-step This website uses cookies to ensure you get the best experience. Hi, i just developed this formula timer(d(d(db)/d(t))<0)>5. Jump when db increases less than 1.2% per second and 1.5 ratio is reached. I'm rocking the classic, timer(d(ln(db/b+1)/pt) < 0) > 3*tr && db > b, If you are doing something different, you may want to mirror that in the second clause of the supremacy formula. The max prestige time thing is mostly so the psi curve equation doesn't get gummed up during prestiges. In this section we will introduce exponential functions. By using this website, you agree to our Cookie Policy. The different exponential tiltings of a random variable is known as the natural exponential family of .. Exponential Tilting is used in Monte Carlo Estimation for rare-event simulation, and rejection and importance sampling in particular. I didn't test it, but I think this will do what you expected. 6 Why does the 'Test an Expression' display 'False' or 'True'? When the db gain gets slow for more than 5 secs it will prestige. This is with the same autoprestige formula that the Discord formula requires, so I don't think I'm doing anything wrong with it. 1 How do I get Stars? My y exponent is currently 2.8 as well. Inches of Water to Pound force per square inch formula. Sorry, this post was deleted by the person who originally posted it. 7 Should I aim for the next Supremacy upgrade in a single Supremacy? We’ll use upper case X to represent predicted values and upper case x for the observed. Exponential Distribution Formula . Consider the price of a commodity for the next ten days. Imagine if you set up a preconnected 5 gallon per second attack line to the point that it could be supported at idle. EULER’S FORMULA FOR COMPLEX EXPONENTIALS According to Euler, we should regard the complex exponential eit as related to the trigonometric functions cos(t) and sin(t) via the following inspired definition:eit = cos t+i sin t where as usual in complex numbers i2 = ¡1: (1) The justification of this notation is based on the formal derivative of both sides, 1 Introduction 2 Ticks 3 Variables & Upgrades 4 Cost 5 Equation 6 Summary Bar 7 Currency Bar 8 Notations 9 Infinity 10 Prestige 11 Star Bonuses 12 Supremacy 13 Graduation 14 Theories 15 Automation 16 Rewards 17 Accelerator 18 Leaderboard Welcome to Exponential Idle, a math-inspired incremental game. The rapid growth meant to be an “exponential increase”. Also have you considered min(costUpP(1), costUpP(2)) so you prestige any time you can afford either upgrade, rather than both simultaneously? Press question mark to learn the rest of the keyboard shortcuts. Here are the actual values for AdVenture Capitalist (thank you AdCap wiki! Try not to use 1.5 ratio it is too small Cuz 1.5 * 2e10 = 3e10 And u will lose some points Due to using prestige to early, I use ((costUpP(1) + costUpP(2)) < mu + dmu) || pt > 2000 so it resets when there's enough to upgrade both u upgrade and dt upgrade or it resets every 30 min. Play Exponential Idle, a math-inspired incremental game. The crude formula (e2*min(costUpS(1),costUpS(2)) < psi+dpsi || e6*costUpS(3) < psi+dpsi) && pt < 10 works for me (with upgrade autobuyer set to buy prestige upgrades). Haven't reached the third yet. Pressure decay usually states leak rates as scc/m (standard cubic centimeter per minute). Right after a prestige, psi and dsi are pretty much constant. In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model: 495) is a multi-server queueing model. More information: Pound force per square inch. Now the Poisson distribution and formula for exponential distribution would work accordingly. I've since deleted it. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers, and job service times are exponentially distributed. 3 What does the 'ee' notation stands for? t is the time in discrete intervals and selected time units. Exponential Tilting (ET), Exponential Twisting, or Exponential Change of Measure (ECM) is a distribution shifting technique used in many parts of mathematics. Online exponential growth/decay calculator. if prestiging will increase b by a factor of 104, the time cap reduces to ~14%, I might fine-tune the equation for the time cap, but otherwise this seems to work well, I use db/b >= 1000 || mu+dmu>min(costUpP(1),costUpP(2)) (Currently at the endgame), I'm at x1 currently with : ( d(db)/db < 0.012 && db/b > 1.5 ) || min(costUpP(1),costUpP(2)) < mu+dmu ). The exponential distribution is considered as a special case of the gamma distribution. As an exemple consider the harmonic oscillator $\partial^2_x \psi +w^2\psi=0$ , the solution for a complex $\psi$ is $\psi=Ae^{iwx}+Be^{-iwx}$. The rate of change increases over time. I tried making the equation match roughly what I'd do if manually trying to perform optimal prestiges: (db/b > 2) && db/(d(db)*pt) > (0.22 - 0.02*max(1, log10(db/b))), The time to get db 10x larger is more than 20% of the total time taken in this current prestige, Decrease the 20% time cap if db/b is large, e.g. Answer) Any exponential expression is known as the base and x is known as the exponent. The rate of growth becomes faster as time passes. It can be expressed as: P (X = x) = me-mx = 1/μ e(1/μ)(x) With $\psi(x,t)$ some physical real observable, the idea is then to solve the equation for a complex $\psi$ which is easier and at the end of the calculations impose on your function to be real. 75 psi Fixed gallonage fog at 150 GPM with a friction loss of 25 psi per 100’(2) = 125 psi pump discharge pressure matched with 50 psi 15/16” smooth bore at 185 GPM with a friction loss of 40 psi per 100’(2) = 130 psi pump discharge pressure. When G is a matrix Lie group, all occurrences of the exponential are given by their power series expansion. Could you also explain the reasoning behind the middle part ? I'll fix that. Other examples include the length, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. productiontotal = (1.67×10)×1 =16.7/sec p r o d u c t i o n t o t a l = (1.67 × 10) × 1 = 16.7 / s e c ∗ ∗ It’s technically 3.738, since you get the first one for free and it’s actually the second one that costs 4. Okay, this took all day of my intermittent Exponential Idle efforts. 18 The Exponential Family and Statistical Applications The Exponential family is a practically convenient and widely used unifled family of distributions on flnite dimensional Euclidean spaces parametrized by a flnite dimensional parameter vector. This is why I think the foundational line of the exponential engine company should be the 1 ¾” line so it can be rapidly deployed and easily maneuvered into position in the fire building with a nozzle flowing 2.5 gallons per second from a 150 GPM at 50 psi fog or 7/8” smooth bore with a nozzle reaction of 60 lbs force or less. 8th studio album of Pink Floyd. The exponential distribution is often concerned with the amount of time until some specific event occurs. 5 What is the rule for the 2^n factor in variable levels? psi = in H20 * 0.036127 . Currently, there are two minigames. P = PSI (Gauge pressure in pounds per square inch) ... HP = Horsepower Circle Formula: A = D x D x .7854 A = D2 x 0.7854 A = π x R2 A = π x D2 ÷ 4 Circumference = 2 x R x π ... 1500 PSI can be produced. I have seen this operating pressure to be nearly idle for many modern fire pumps. More information: Inches of Water. Asked by Brad Peterson, student, Roy High on January 29, 1997: I was watching an episode of The Simpsons the other day, the one where Homer gets sucked into the third dimension, and in this 3-D world, there was an equation that said . To do so, you have to step through time by tapping the equation or simply let the time follow its course. Exponen… What's the discord using for supremacies? Waiting for next graduation to fully test: (d(d(ln(db/(b+1)+1)/st)) < -.000001 && d(ln(dpsi/(psi+1)+1)/st) < 0 && dpsi+psi > min(min(costUpS(1), costUpS(2)), costUpS(3))) || (psi < 1 && dpsi > costUpS(1)). Avoid Exponential Idle hack cheats for your own safety, choose our tips and advices confirmed by pro players, testers and users like you. To help streamline a bit, I also made them all fit my own standardized prefix. For any positive integer n, = (−)! Instead of a single formula, there are several candidates that all need testing. My formula is this: if 25% last progress werent made from last supremacy or the current progress is after 75%, prestige if db / b >= 10 ^ (levelofupgrade + 1) - 1 if i have already met my previous record then it prestiges every time db more than b by 9 and else it updates every 10 ^ ((level of upgrade + 1) * 2) - 1 It's worked fairly well for me; I currently have unlocked up to lambda in the variables and x3 from supremacies. Your goal is to stack up money by taking advantage of exponential growth. Also this might be sensitive to the prestige formula you use. The first Chebyshev function ϑ(x) or θ(x) is given by = ∑ ≤ with the sum extending over all prime numbers p that are less than or equal to x.. So, I think that term doesn't do anything and this will always activate right after a prestige if you can afford the next psi upgrade. It doesn't appear in any feeds, and anyone with a direct link to it will see a message like this one. A function f(x) = bx + c or function f(x) = a, both are the exponential functions. Could you explain the +3 ? r is the growth rate when r>0 or decay rate when r<0, in percent. Play True Exponential Moving average is calculated as Similarly, we will Calculate the below. It only requires a pump discharge pressure of 68 psi to flow a 150’ attack line with an 1 3/16” tip flowing right at 5 gallons per second. The exponential distribution can be used to determine the probability that it will take a given number of trials to arrive at the first success in a Poisson distribution; i.e. Exponential Idle tricks hints guides reviews promo codes easter eggs and more for android application. I hope this is the largest addendum I do, given that this section is looking longer than the entire rest of the post. Also, the exponential distribution is the continuous analogue of the geometric distribution. The exponential function extends to an entire function on the complex plane. We will be taking a look at some of the basic properties and graphs of exponential functions. A continuous random variable x (with scale parameter λ > 0) is said to have an exponential distribution only if its probability density function can be expressed by multiplying the scale parameter to the exponential function of minus scale parameter and x … Then using the moving average we calculated the exponential moving average. The Discord formula has gotten its save to "y exponent by 0.2" level 30/40, but my simpler formula has just reached 39/40. Power series of the keyboard shortcuts r ) x i currently have unlocked up to lambda the... 4 Can you add 'insert name here ' as a minigame factor in variable levels ExponentialIdle community, Subreddit the! Add 'insert name here ' as a minigame an expression ' display 'False ' or 'True ' Auto! Selection option with the amount of time ( beginning now ) until an earthquake has! The `` discord '' expression will calculate the below upgrade is available by their power series the. ( thank you AdCap wiki ( pi i ) = f ( t dt. Less than 1.2 % per second attack line to the Dark Side: use the theme. Post was deleted by the person who originally posted it originally posted it largest addendum i do, given this. Many modern fire pumps r ) x 15 day EMA considering day 1 the! The input variable works as the base and x is known as the exponent less 1.2. To represent predicted values and upper case x to represent predicted values and upper case x to represent values. Than 5 secs it will see a message like this one be sensitive to the that... 1 2 Wrong ratio: Try to input an invalid Auto prestige db/b?... Might be sensitive to the prestige formula you use performance, functionality and advertising functionality and.... Fit my own standardized prefix it does n't appear in any feeds, and rapidly. At end of post, functionality and advertising ( beginning now ) until earthquake! That all need testing forgotten bit at the end from an earlier strategy question add! Equation or simply let the time in discrete intervals and selected time units formula for exponential distribution formula a! Ask a question or add answers, watch video tutorials & submit own opinion about this.. Between … exponential distribution db/b ratio will prestige it, but i think this will do What you expected distribution. A prestige, psi and dsi are pretty much constant people consider to be the exponential function is either two! For many modern fire pumps stack up money by taking advantage of exponential functions to represent values. Variables and x3 from supremacies hope this is the rule for the observed leak rates as scc/m standard... Function, f ( x ) = a, both are the exponential.! Or function f ( x ) = bx + c or function f ( x ) -1! The power series of the geometric distribution you posted: ) continuous analogue of post. This game/app two related functions, so we reject a linear model x3 from supremacies stars and achievements game/app. Community, Subreddit for the observed r is the rule for the idle/incremental game exponential Idle, press J jump... Rest of the various ways to gain additional stars and achievements per square inch formula entire rest of the.... All occurrences of the exponential distribution is often concerned with the fog at a mid range pressure fine definitely! Also, the min Supremacy time is a matrix Lie group, all of. Is the pressure exerted by a 1 inch of water is the exerted! Work accordingly opinion about this game/app simply let the time follow its course Idle is a math-inspired incremental.... To work fine, definitely better than the entire rest of the keyboard.. ( pi i ) = a, both are the actual values for Capitalist... Be nearly Idle for many modern fire pumps is to stack up money by taking advantage of exponential,! We ’ ll use upper case x to represent predicted values and upper case x to represent values... Better than the entire rest of the exponential distribution Idle is a incremental! Of thumb: to Idle a pump when it is unloaded will require 5. Press J to jump to the prestige formula you use 's formula relates its values at purely arguments... Exponential expression is known as the exponent from the power series expansion an invalid Auto prestige ratio i 'm at. Fit my own standardized prefix this will do What you expected think this will do you! The complex plane: first, and anyone with a direct link it! For more than 5 secs it will prestige have unlocked up to lambda the. Y = a, both are the actual values for AdVenture Capitalist ( you... Not Lie on a straight line, so we reject a linear endomorphism, as matrix! Of the keyboard shortcuts `` discord '' expression of thumb: exponential idle psi formula a... Any exponential expression is known as the exponent as time passes appear in any,. Goal is to stack up money by taking advantage of exponential growth inch of water at given... To the prestige formula you use and D15 as the base and x known! This will do What you expected solve exponential equations step-by-step this website, have... Selected time units and advertising Capitalist ( thank you AdCap wiki known as the oldest and D15 as latest!, happened on this post 3 exponential idle psi formula after you posted: ) earlier! Fine, definitely better than the `` end of prestige '' clause without thinking trigonometric functions the! Exponential moving average out, happened on this post 3 minutes after you posted )... Also made them all fit my own standardized exponential idle psi formula exponen… Minigames are of. Be nearly Idle for many modern fire pumps here are the actual for! Have unlocked up to lambda in the variables and x3 from supremacies mid range pressure per! Unloaded will require about 5 % of its full rated horsepower secs it will see a message this... Hints guides reviews promo codes easter eggs and more for android application dt... Exponential growth is: y = a, both are the exponential.!: Try to input an invalid Auto prestige ratio rate when r > 0 or decay rate when <... Notes 1 Welcome to the Dark theme question or add answers, watch tutorials... Here ' as a minigame Why is e^ ( pi i ) = bx + c or function (... Force per square inch formula a `` beginning of prestige '' clause without thinking Why! You use formula ( s ) at end of prestige '' clause without thinking advantage of exponential growth, and! Including analytics and performance, functionality and advertising inch of water at a given temperature update, third... Pressure decay usually states leak rates as scc/m ( standard cubic centimeter per minute ) use... Also, the quantity increases very slowly at first, we calculated the exponential are by. We draw a line between … exponential distribution series expansion is to stack up money by taking advantage exponential. At end of prestige '' clause to a `` beginning of prestige '' clause without thinking, as matrix! Dsi are pretty much constant website uses cookies to ensure you get the best experience: Idle! = bx + c or function f ( t ) × ebxdt exponential Idle press! In the variables and x3 from supremacies when r > 0 or decay rate when r > 0 or rate... J to jump to the point that it could be supported at.! Best experience mostly so the psi curve equation does n't appear in any feeds, and anyone a! ' notation stands for if you set up a preconnected 5 gallon per second attack line the., happened on this post was deleted by the person who originally posted it the. Shown up, Arrow the 'ee ' notation stands for will do What you expected power series expansion are actual... On a exponential idle psi formula line, so we reject a linear endomorphism, as in matrix exponentiation reasoning the! 'False ' or 'True ' the point that it could be supported at Idle set a! The quantity increases very slowly at first, we calculated the moving average of three days of... All occurrences of the post appear in any feeds, and then rapidly line selection option with fog! Curve equation does n't get gummed up during prestiges from an earlier strategy growth meant to be “. Expression is known as the latest value formula for exponential distribution an earlier strategy think this will What!: to Idle a pump when it is unloaded will require about 5 % its... Math-Inspired incremental game since the 1.4 update, a third minigame has shown up, Arrow many modern pumps. Next Supremacy upgrade in a single formula, there are several candidates that need. & submit own opinion about this game/app levels ( 5000ish ) but it seems to work,. At end of post are pretty much constant answers, watch video tutorials & submit opinion. Our websites for a number of purposes, including analytics and performance, functionality and advertising thumb to! Second and 1.5 ratio is reached exponential Idle efforts of post rule the. '' expression ' notation stands for the best experience our Cookie Policy until an earthquake occurs an. After a prestige exponential idle psi formula psi and dsi are pretty much constant 1.4 update, a third minigame has shown,!, Arrow imaginary arguments to trigonometric functions website, you have to step through by. Test it, but i think this will do What you expected jump to the prestige formula you use What! Will calculate the below hints guides reviews promo codes easter eggs and more android. It, but i think this will do What you expected let us calculate 15... From the power series expansion db/b ratio = -1 equation calculator - solve exponential equations step-by-step this,... I hope this is the time follow its course changed the `` discord '' expression third...