Question

Solve each equation.

$e^{3x}=4$

Short answer

The solution to the equation is$\frac{1}{3}\ln \left(4\right)$ .

Step-by-step solution

Step 1. Given Information.

Given equation is $e^{3x}=4$

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l}{e}^{3x}=4\\ \ln \left(e^{3x}\right)=\ln \left(4\right)\\ 3x=\ln \left(4\right)\\ x=\frac{1}{3}\ln \left(4\right)\end{array}$

Step 3. Conclusion.

Hence, the solution to the equation is$x=\frac{1}{3}\ln \left(4\right)$$x=\frac{1}{3}\ln \left(4\right)$.