Precalculus Examples

$\log_{4} (\frac{x^{4}}{y^{7}})$

Step 1

Rewrite $\log_{4} (\frac{x^{4}}{y^{7}})$ as $\log_{4} (x^{4}) - \log_{4} (y^{7})$ .

$\log_{4} (x^{4}) - \log_{4} (y^{7})$

Step 2

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

$4 \log_{4} (x) - \log_{4} (y^{7})$

Step 3

Expand $\log_{4} (y^{7})$ by moving $7$ outside the logarithm.

$4 \log_{4} (x) - (7 \log_{4} (y))$

Step 4

Multiply $7$ by $- 1$ .

$4 \log_{4} (x) - 7 \log_{4} (y)$