Q 99. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

$e^{3x}=10$

Step-by-Step Solution

Answer

The solution to the equation, $e^{3x}=10$is, $x=\frac{1}{3}\ln 10$.

Step 1. Given Information

The given equation to be solved is $e^{3x}=10$.

Step 2. Formula used

Rule of change from logarithm to exponents: 

${\log }_{a}b=y\Rightarrow a^y=b$

Step 3. Finding Solution

The given equation is $e^{3x}=10$.

Take logarithm on both sides.

$$\begin{gathered} \ln e^{3x}=\ln 10 \\ 3x\ln e=\ln 10 \\ 3x=\ln 10 \\ x=\frac{1}{3}\ln 10 \end{gathered}$$

The solution to the given equation is, $x=\frac{1}{3}\ln 10$.