Precalculus Examples

$\log_{6} ({(x y^{3})}^{6})$

Step 1

Expand $\log_{6} ({(x y^{3})}^{6})$ by moving $6$ outside the logarithm.

$6 \log_{6} (x y^{3})$

Step 2

Rewrite $\log_{6} (x y^{3})$ as $\log_{6} (x) + \log_{6} (y^{3})$ .

$6 (\log_{6} (x) + \log_{6} (y^{3}))$

Step 3

Expand $\log_{6} (y^{3})$ by moving $3$ outside the logarithm.

$6 (\log_{6} (x) + 3 \log_{6} (y))$

Step 4

Apply the distributive property.

$6 \log_{6} (x) + 6 (3 \log_{6} (y))$

Step 5

Multiply $3$ by $6$ .

$6 \log_{6} (x) + 18 \log_{6} (y)$