Answer
$x=\dfrac{\log\dfrac{1}{2}+\log5}{\log5}\\\\
x\approx0.5693
$
Work Step by Step
Getting the logarithm of both sides and then using the properties of logarithms, the value of $x$ in the expression $
5^{x-1}=\dfrac{1}{2}
$ is
\begin{array}{l}
\log5^{x-1}=\log\dfrac{1}{2}\\\\
(x-1)\log5=\log\dfrac{1}{2}\\\\
x\log5-\log5=\log\dfrac{1}{2}\\\\
x\log5=\log\dfrac{1}{2}+\log5\\\\
x=\dfrac{\log\dfrac{1}{2}+\log5}{\log5}\\\\
x\approx0.5693
.\end{array}
