Question

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

$e^{x-1}+4=12$

Short answer

On solving the given exponential equation, the exact answer is$\ln \left(8\right)+1$and the approximate answer is$3.079$.

Step-by-step solution

Step 1. Given information.

Consider the given exponential equation,

$e^{x-1}+4=12$

Subtract $4$from both sides,

$e^{x-1}=8$

Take natural logarithm on both sides,

$\ln \left(e^{x-1}\right)=\ln \left(8\right)$

Step 2. Use the power property.

Using the power property,

$$\begin{gathered} \left(x-1\right)\ln \left(e\right)=\ln \left(8\right) \\ x-1=\ln \left(8\right) \end{gathered}$$

Add $1$on both sides,

localid="1644940170151" $$\begin{gathered} x=\ln \left(8\right)+1 \\ x\approx 3.079 \end{gathered}$$