Precalculus Examples

$\log_{4} ({(x y^{3})}^{4})$

Step 1

Expand $\log_{4} ({(x y^{3})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{4} (x y^{3})$

Step 2

Rewrite $\log_{4} (x y^{3})$ as $\log_{4} (x) + \log_{4} (y^{3})$ .

$4 (\log_{4} (x) + \log_{4} (y^{3}))$

Step 3

Expand $\log_{4} (y^{3})$ by moving $3$ outside the logarithm.

$4 (\log_{4} (x) + 3 \log_{4} (y))$

Step 4

Apply the distributive property.

$4 \log_{4} (x) + 4 (3 \log_{4} (y))$

Step 5

Multiply $3$ by $4$ .

$4 \log_{4} (x) + 12 \log_{4} (y)$