Thread: Logarithm Proof

Show that $\displaystyle \frac {\log_a x}{\log_\frac{a}{b}x} = 1 + \log_a\frac{1}{b}$.

I have no idea where to begin. I know some of the property rules of logarithms but, that did not help. Any ideas?

Use the property that $\displaystyle \log_a b=\frac{\log b}{\log a}$

Originally Posted by watchmath

Use the property that $\displaystyle \log_a b=\frac{\log b}{\log a}$

Ok here's what I got so far. Working on the one side only I get
$\displaystyle \frac {\log 1}{\log a}-\frac {\log b}{\log a} +1 = \frac {\log_a x}{\log_\frac{a}{b}x}$
That's as far as I got.