Answer
$x=0.805$
Work Step by Step
$6(2^{3x-1})-7=9$
$6(2^{3x-1})=16$
$2^{3x-1}=\frac{16}{6}=\frac{8}{3}$
$\log_22^{3x-1}=\log_2\frac{8}{3}$ (Use the Inverse Property: $\log_aa^x=x$):
$3x-1=\log_2\frac{8}{3}=\frac{\ln\frac{8}{3}}{\ln2}=\frac{\ln8-\ln3}{\ln2}$
$3x=\frac{\ln8-\ln3}{\ln2}+1$
$x=\frac{\frac{\ln8-\ln3}{\ln2}+1}{3}=0.805$
