# How do you simplify 7 log_3 k + 6 log_3 m – 9 log_3 n?

Jun 25, 2015

Adding logs (with the same ground number) is like multiplying the arguments.

#### Explanation:

And subtraction boils down to division.

But first we must get the coefficients behind the log, remembering that $n \cdot \log x = \log {x}^{n}$

$= {\log}_{3} {k}^{7} + {\log}_{3} {m}^{6} - {\log}_{3} {n}^{9}$

Since they are all ${\log}_{3}$ we may then multiply and divide the arguments:

$= {\log}_{3} \left(\frac{{k}^{7} \cdot {m}^{6}}{n} ^ 9\right)$