Question

Solve each equation.

$3e^x-2=0$

Short answer

The solution to the equation is$\ln \left(\frac{2}{3}\right)$.

Step-by-step solution

Step 1. Given Information.

Given equation is $3e^x-2=0$

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l}3e^x-2=0\\ 3e^x=2\\ e^x=\frac{2}{3}\\ \ln \left(e^x\right)=\ln \left(\frac{2}{3}\right)\\ x=\ln \left(\frac{2}{3}\right)\end{array}$

Step 3. Conclusion.

Hence, the solution to the equation is $x=\ln \left(\frac{2}{3}\right)$.