#### Answer

$x=4$

#### Work Step by Step

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}