How to show that $- \log_b x = \log_{\frac{1}{b}} x$ I saw the following log rule and have been struggling to show it's true, using the change of base rule. Any hints for proving it would be much appreciated. 
$- \log_b x = \log_{\frac{1}{b}} x$
I get as far as showing that $- \log_b x = \log_b \frac{1}{x}$ and think the change of base rule for logs, $\log_b x = \frac{\log_c x}{\log_c b} $ might be useful, but am not sure how to proceed. 

$$\log_{1/b} x=\frac{\log_b x}{\log_b \frac{1}{b}}=\frac{\log_b x}{-1}=-\log_b x$$
