Question

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

$e^{x+1}+2=16$

Short answer

On solving the given exponential equation, the exact answer is$\ln \left(14\right)-1$and the approximate answer is$1.639$.

Step-by-step solution

Step 1. Given information.

Consider the given exponential equation,

$e^{x+1}+2=16$

Subtract $2$from both sides,

$e^{x+1}=14$

Take natural logarithm on both sides,

$\ln \left(e^{x+1}\right)=\ln \left(14\right)$

Step 2. Use the power property.

Using the power property,

$$\begin{gathered} \left(x+1\right)\ln \left(e\right)=\ln \left(14\right) \\ x+1=\ln \left(14\right) \end{gathered}$$

Subtract $1$from both sides,

role="math" localid="1644939765622" $$\begin{gathered} x=\ln \left(14\right)-1 \\ x\approx 1.639 \end{gathered}$$