Simplify/Condense 4 log base 3 of u-20 log base 3 of v

$4 \log_{3} (u) - 20 \log_{3} (v)$

Step 1

Simplify each term.

Simplify $4 \log_{3} (u)$ by moving $4$ inside the logarithm.

$\log_{3} (u^{4}) - 20 \log_{3} (v)$

Simplify $- 20 \log_{3} (v)$ by moving $20$ inside the logarithm.

$\log_{3} (u^{4}) - \log_{3} (v^{20})$

Step 2

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

$\log_{3} (\frac{u^{4}}{v^{20}})$