Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set - Page 726: 10

$x=\frac{5}{2}$

Note that: $4=2^2$ AND $32=2^5$ Write each side with a base of $2$ to obtain: $(2^2)^{x}=2^5 \\2^{2x}=2^5$ RECALL: If $a^x = a^y$, then $x=y$. Use the rule above to obtain: $2^{2x}=2^5 \\2x=5 \\x=\frac{5}{2}$