Precalculus Examples

$\log_{8} ({(\frac{x}{y^{2}})}^{4})$

Step 1

Expand $\log_{8} ({(\frac{x}{y^{2}})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{8} (\frac{x}{y^{2}})$

Step 2

Rewrite $\log_{8} (\frac{x}{y^{2}})$ as $\log_{8} (x) - \log_{8} (y^{2})$ .

$4 (\log_{8} (x) - \log_{8} (y^{2}))$

Step 3

Expand $\log_{8} (y^{2})$ by moving $2$ outside the logarithm.

$4 (\log_{8} (x) - (2 \log_{8} (y)))$

Step 4

Multiply $2$ by $- 1$ .

$4 (\log_{8} (x) - 2 \log_{8} (y))$

Step 5

Apply the distributive property.

$4 \log_{8} (x) + 4 (- 2 \log_{8} (y))$

Step 6

Multiply $- 2$ by $4$ .

$4 \log_{8} (x) - 8 \log_{8} (y)$