Question

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

$4e^{x+1}=16$

Short answer

On solving the given exponential equation, the exact answer is $\ln \left(4\right)-1$and the approximate answer is$0.386$.

Step-by-step solution

Step 1. Given information.

Consider the given exponential equation,

$4e^{x+1}=16$

Divide both sides by $4$,

$e^{x+1}=4$

Take natural logarithm on both sides,

$\ln \left(e^{x+1}\right)=\ln \left(4\right)$

Step 2. Use the power property.

Using the power property,

$$\begin{gathered} \left(x+1\right)\ln \left(e\right)=\ln \left(4\right) \\ x+1=\ln \left(4\right) \\ x=\ln \left(4\right)-1 \\ x\approx 0.386 \end{gathered}$$