Multiplication Rule for Logarithm Bases
Yes there is.
To derive it use the change of base rule
\[log_a b = \frac{log_x b }{log_x a }\]
.If
\[x=b\]
then \[log_a b = \frac{log_b b }{log_b a } = \frac{1}{log_ba}\]
.Suppose the that we want to simplify
\[log_m u+ log_nu\]
.Using the change of base rule as above gives
\[\frac{1}{log_u m}+ \frac{1}{log_u n}= \frac{log_um+log_un}{log_um log_un}= \frac{log_u (mn)}{log_um log_un}\]
. 
