Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

In Problems $1-6$, solve each equation.

$3^x=e$.

Step-by-Step Solution

Answer

The solution of the equation $3^x=e$ is, $x=\frac{1}{\ln 3}$.

Step 1 Given equation is,

$3^x=e$.

The above equation can be solved by applying logarithm to the base $e$ on both sides of the equation.

$\ln \left(3^x\right)=\ln \left(e\right)$

Step 2 Now simplify the obtained equation.

$$\begin{gathered} x \ln 3=1 \\ x=\frac{1}{\ln 3} \end{gathered}$$

Hence the required solution is,$x=\frac{1}{\ln 3}$.