Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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