Simplify/Condense 6 log base 3 of u+6 log base 3 of v

$6 \log_{3} (u) + 6 \log_{3} (v)$

Step 1

Simplify each term.

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

$\log_{3} (u^{6}) + 6 \log_{3} (v)$

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

$\log_{3} (u^{6}) + \log_{3} (v^{6})$

Step 2

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

$\log_{3} (u^{6} v^{6})$