Simplify/Condense 7 log base 3 of k+6 log base 3 of m-9 log base 3 of n

$7 \log_{3} (k) + 6 \log_{3} (m) - 9 \log_{3} (n)$

Simplify each term.

Simplify $7 \log_{3} (k)$ by moving $7$ inside the logarithm.

$\log_{3} (k^{7}) + 6 \log_{3} (m) - 9 \log_{3} (n)$

Simplify $6 \log_{3} (m)$ by moving $6$ inside the logarithm.

$\log_{3} (k^{7}) + \log_{3} (m^{6}) - 9 \log_{3} (n)$

Simplify $- 9 \log_{3} (n)$ by moving $9$ inside the logarithm.

$\log_{3} (k^{7}) + \log_{3} (m^{6}) - \log_{3} (n^{9})$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (k^{7} m^{6}) - \log_{3} (n^{9})$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{k^{7} m^{6}}{n^{9}})$