I know it might be a simple question to answer but I am not able to figure out how do I solve such equation for complex cases. I want to solve the equation manually, I tried solving it using the identity
$\log (z^w) = w\log (z) + 2I \pi n$ as mentioned here but I think I am getting something wrong. How do I use log identities for complex cases and solve the equation? I searched about complex logarithm but could not figure out how to use here to get the result.
The answer for the equation $4^{5 - 9*x} - 8^{2 -x} = 0$ is $\frac {log(16) + 2I \pi n}{log(32768)}$ as computed here