Answer
$x=3+\dfrac{\log5}{\log2}\approx5.3219$
Work Step by Step
$2^{x-3}=5$
Apply $\log$ to both sides of the equation:
$\log2^{x-3}=\log5$
Take $x-3$ down to multiply in front of its respective $\log$:
$(x-3)\log2=\log5$
Solve for $x$:
$x-3=\dfrac{\log5}{\log2}$
$x=3+\dfrac{\log5}{\log2}\approx5.3219$
