Precalculus Examples

$\log_{4} (\frac{x^{5}}{y^{8}})$

Step 1

Rewrite $\log_{4} (\frac{x^{5}}{y^{8}})$ as $\log_{4} (x^{5}) - \log_{4} (y^{8})$ .

$\log_{4} (x^{5}) - \log_{4} (y^{8})$

Step 2

Expand $\log_{4} (x^{5})$ by moving $5$ outside the logarithm.

$5 \log_{4} (x) - \log_{4} (y^{8})$

Step 3

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

$5 \log_{4} (x) - (8 \log_{4} (y))$

Step 4

Multiply $8$ by $- 1$ .

$5 \log_{4} (x) - 8 \log_{4} (y)$