Precalculus Examples

$5 \log_{6} (w) + \frac{\log_{6} (u)}{3}$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \log_{6} (w)$ by moving $5$ inside the logarithm.

$\log_{6} (w^{5}) + \frac{\log_{6} (u)}{3}$

Step 1.2

Rewrite $\frac{\log_{6} (u)}{3}$ as $\frac{1}{3} \log_{6} (u)$ .

$\log_{6} (w^{5}) + \frac{1}{3} \log_{6} (u)$

Step 1.3

Simplify $\frac{1}{3} \log_{6} (u)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{6} (w^{5}) + \log_{6} (u^{\frac{1}{3}})$

Step 2

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

$\log_{6} (w^{5} u^{\frac{1}{3}})$