Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 37

$x=-1.710$

$3^x=2^{x-1}$ $3^x=2^x·2^{-1}$ $\frac{3^x}{2^x}=\frac{1}{2}$ $(\frac{3}{2})^x=\frac{1}{2}$ $\log_{\frac{3}{2}}(\frac{3}{2})^x=\log_{\frac{3}{2}}\frac{1}{2}$ $x=\log_{\frac{3}{2}}\frac{1}{2}=\frac{\ln\frac{1}{2}}{\ln\frac{3}{2}}=-1.710$