# How do you condense  log_6 25 - log_6 5 ?

Mar 15, 2016

Since the log's are in the same base, you can immediately condense using the rule ${\log}_{a} n - {\log}_{a} m = {\log}_{a} \left(\frac{n}{m}\right)$

#### Explanation:

${\log}_{6} \left(25\right) - {\log}_{6} \left(5\right) = {\log}_{6} \left(\frac{25}{5}\right) = {\log}_{6} \left(5\right)$

Practice exercises:

1. Condense ${\log}_{5} \left(x + 4\right) + {\log}_{5} \left(2 x - 1\right)$

Challenge problem:

Using the log rule ${\log}_{a} \left(n\right) = \frac{\log n}{\log a}$ and the multiplication/division rules shown earlier simplify the following expression completely.

${\log}_{2} \left(20\right) - {\log}_{4} \left(5\right)$

Hopefully this helps!