Precalculus Examples

$\log_{5} (\frac{x^{5}}{y^{7}})$

Step 1

Rewrite $\log_{5} (\frac{x^{5}}{y^{7}})$ as $\log_{5} (x^{5}) - \log_{5} (y^{7})$ .

$\log_{5} (x^{5}) - \log_{5} (y^{7})$

Step 2

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

$5 \log_{5} (x) - \log_{5} (y^{7})$

Step 3

Expand $\log_{5} (y^{7})$ by moving $7$ outside the logarithm.

$5 \log_{5} (x) - (7 \log_{5} (y))$

Step 4

Multiply $7$ by $- 1$ .

$5 \log_{5} (x) - 7 \log_{5} (y)$