Question

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

$e^x=8$

Short answer

The exact solution of the exponential equation $e^x=8$is $x=\ln \left(8\right)$and the approximate solution is $2.079$which is rounded to three decimal places.

Step-by-step solution

Step 1. Given

An exponential equation$e^x=8$

To solve the exponential equation

Step 2. Take natural logarithm on both sides

Since the exponential is isolated, take the natural logarithm of both sides.

$\ln \left(e^x\right)=\ln \left(8\right)$

Step 3. Use the Power Property

Use the Power Property to get the $x$as a factor, not an exponent.

$x\ln \left(e\right)=\ln \left(8\right)$

Step 4. Solve for x 

Solve for $x$and find the exact answer.

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

Step 5. Approximate the answer

$$\begin{gathered} x=\ln \left(8\right) \\ =2.079 \end{gathered}$$