Question

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

$3e^{x+2}=9$

Short answer

On solving the given exponential equation, the exact answer is $\ln \left(3\right)-2$and the approximate answer is $-0.0901$.

Step-by-step solution

Step 1. Given information.

Consider the given exponential equation,

$3e^{x+2}=9$

Divide both sides by $3$,

$e^{x+2}=3$

Take natural logarithm on both sides,

$\ln \left(e^{x+2}\right)=\ln \left(3\right)$

Step 2. Use the power property,

Using the power property,

$$\begin{gathered} \left(x+2\right)\ln \left(e\right)=\ln \left(3\right) \\ x+2=\ln \left(3\right) \\ x=\ln \left(3\right)-2 \\ x\approx -0.0901 \end{gathered}$$