Answer
$x \approx 2.60$
Work Step by Step
Take the natural log of both sides to obtain:
$\ln{(2^{3x-5})} = \ln{7}$
Use the rule $\ln{(a^n)} = n\cdot\ln{a}$ to obtain:
$(3x-5)\ln{2} = \ln{7}$
Divide $\ln{2}$ to both sides of the equation to obtain:
$\dfrac{(3x-5)\ln2}{\ln2} = \dfrac{\ln7}{\ln2}
\\3x-5=\dfrac{\ln7}{\ln2}$
Add $5$ on both sides of the equation to obtain:
$3x=5+\dfrac{\ln7}{\ln2}$
Divide $3$ on both of the equation to obtain:
$x = \dfrac{5+\frac{\ln7}{\ln2}}{3}$
Use a calculator to obtain:
$x \approx 2.60$