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

$x=\dfrac{3}{2}$

Using the laws of exponents, the given equation, $ 9^x=27 ,$ is equivalent to \begin{array}{l}\require{cancel} (3^2)^x=3^3 \\\\ 3^{2x}=3^3 .\end{array} Since the bases are the same, the exponents can be equated. Hence, \begin{array}{l}\require{cancel} 2x=3 \\\\ x=\dfrac{3}{2} .\end{array}