Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 16

$x=4$

Using exponents, the given equation, $ 2^{x-1}=8 ,$ is equivalent to \begin{array}{l}\require{cancel} 2^{x-1}=2^3 .\end{array} Since the bases are the same, the exponents can be equated. Hence, \begin{array}{l}\require{cancel} x-1=3 \\\\ x=3+1 \\\\ x=4 .\end{array}