Answer
$x=\frac{1}{3}(5+\frac{\log 7}{\log 2})\approx 2.602452$
Work Step by Step
$2^{3x-5}=7$
$(3x-5) \log 2 = \log 7$
$3x\log2-5\log2=\log7$
$3x\log2=5\log2+\log7$
$x=\frac{5\log2+\log7}{3\log 2}$
$x=\frac{1}{3}(5+\frac{\log 7}{\log 2})\approx 2.602452$
