Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 37

$\{ln\frac{3}{2} \}$

Step 1. Let $u=e^x$, we have $2u^2+u-6=0$ or $(u+2)(2u-3)=0$ Step 2. For $u=-2$, we have $e^x=-2$, no solution. Step 3. For $u=\frac{3}{2}$, we have $e^x=\frac{3}{2}$, thus $x=ln\frac{3}{2}$ Step 4. Write the answers in set form $\{ln\frac{3}{2} \}$