Precalculus Examples

$\log_{5} (\frac{x^{8} y^{7}}{2})$

Step 1

Rewrite $\log_{5} (\frac{x^{8} y^{7}}{2})$ as $\log_{5} (x^{8} y^{7}) - \log_{5} (2)$ .

$\log_{5} (x^{8} y^{7}) - \log_{5} (2)$

Step 2

Rewrite $\log_{5} (x^{8} y^{7})$ as $\log_{5} (x^{8}) + \log_{5} (y^{7})$ .

$\log_{5} (x^{8}) + \log_{5} (y^{7}) - \log_{5} (2)$

Step 3

Expand $\log_{5} (x^{8})$ by moving $8$ outside the logarithm.

$8 \log_{5} (x) + \log_{5} (y^{7}) - \log_{5} (2)$

Step 4

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

$8 \log_{5} (x) + 7 \log_{5} (y) - \log_{5} (2)$