Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 38

$\{ln\frac{1}{3} \}$

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