#Exponential equation calculator how to
The image below shows a summary of how to solve the exponential equation in steps. This is the exact answer but it can be evaluated on a calculator as 𝑥 ≈ 1.51. To solve for 𝑥, we simply divide both sides of the equation by (log5-log2). Therefore the equation becomes 𝑥(log5-log2) = 2log2. Now the 𝑥 terms are on one side of the equation, we can factorise 𝑥 out. We subtract 𝑥log2 from both sides of the equation which gives us: We need to gather the 𝑥 terms all together on one side of the equation. Now the bracket is expanded, the equation becomes 𝑥log5 = 𝑥log2 + 2log. Log(5 𝑥) = log(2 𝑥+2) becomes 𝑥log(5) = (𝑥+2)log2.Įxpanding the bracket on the right hand side of the equation, (𝑥+2)log2 becomes 𝑥log2 +2log2. Use the log law log(a b) = blog(a) to bring the powers down in front of the logs on both sides. Bring down the exponent in front of the logs Write each side of the equation inside a log.ĥ 𝑥 = 2 𝑥+2 becomes log(5 𝑥) = log(2 𝑥+2). Bring down the exponent in front of the logs.įor example solve the exponential equation 5 𝑥 = 2 𝑥+2.Take logarithms of both sides of the equation.
How to Solve Exponential Equations with Different Bases To solve an exponential equation with different bases: The power of 2x can be written in front of the log so that log(3 2x) = log(0.51) becomes 2xlog(3) = log(0.51).Ģxlog(3) = log(0.51) can be solved by dividing both sides by 2log(3). Solving an Exponential Equation: Example 2ģ 2x = 0.51 becomes log(3 2x) = log(0.51). This can be evaluated on a calculator to get 𝑥 ≈ 1.59. Xlog(5) = log(13) can be solved for x by dividing both sides of the equation by log(5). The power of x can be written in front of the log so that log(5 x) = log(13) becomes xlog(5) = log(13). Solving an Exponential Equation: Example 1 The resulting linear equation can be solved for x. How to Solve an Exponential Equation To solve an exponential equation, take logs of both sides of the equation and bring the power down in front of the log.
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