Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 9

$x=2$

Using exponents, the given equation, $ 3^{2x}=81 ,$ is equivalent to \begin{array}{l}\require{cancel} 3^{2x}=3^4 .\end{array} Since the bases are the same, the exponents can be equated. Hence, \begin{array}{l}\require{cancel} 2x=4 \\\\ x=\dfrac{4}{2} \\\\ x=2 .\end{array}