Question

Write as a single log with base 2:

\(\log_2 x - \log_8 x\)

I know the base change formula, which turns \(\log_8 x\) into \(\frac{\log_2 x}{\log_2 8}\) but I don't know what to do with it. If I substitute it back in to the equation, then \[\log_2 x - \frac{\log_2 x}{\log_2 8}\]
I'd think I could turn that into one log by using the log rules:
\[\log_2(\frac{8x}{x})\] but that cancels the x which doesn't give me the right answer.