Answer
$x = \frac{\frac{\ln 45}{\ln 2} + 7}{3} \approx 4.164$
Work Step by Step
$2^{3x-7} = 45$
$3x - 7 = \ln_2 45$
$3x = \log_2 45 + 7$
$x = \frac{\log_2 45 + 7}{3}$
$x = \frac{\frac{\ln 45}{\ln 2} + 7}{3}$
$x \approx 4.164$
Check:
$2^{3(\frac{\frac{\ln 45}{\ln 2} + 7}{3})-7} \overset{?}{=} 45$
$2^{\frac{\ln 45}{\ln 2} + 7-7} \overset{?}{=} 45$
$2^{\frac{\ln 45}{\ln 2} } \overset{?}{=} 45$
$45 = 45$
