Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 11

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

Using the laws of exponents, the given equation, $ 4^x=32 ,$ is equivalent to \begin{array}{l}\require{cancel} (2^2)^x=2^5 \\\\ 2^{2x}=2^5 .\end{array} Since the bases are the same, the exponents can be equated. Hence, \begin{array}{l}\require{cancel} 2x=5 \\\\ x=\dfrac{5}{2} .\end{array}