Log solve for x

$7\times2^{3x-5} = 53\\ 2^{3x-5}=\dfrac{53}{7}\\ \log_2 (2^{3x-5})=\log_2\dfrac{53}{7}\\ 3x - 5 = \log_2\dfrac{53}{7}\\ x = \dfrac{\log_2\dfrac{53}{7}+5}{3}$

Which is 7.920565532505595