Precalculus Examples

$\log (\frac{x^{16} y^{12}}{z^{8}})$

Rewrite $\log (\frac{x^{16} y^{12}}{z^{8}})$ as $\log (x^{16} y^{12}) - \log (z^{8})$ .

$\log (x^{16} y^{12}) - \log (z^{8})$

Expand $\log (z^{8})$ by moving $8$ outside the logarithm.

$\log (x^{16} y^{12}) - (8 \log (z))$

Multiply $8$ by $- 1$ .

$\log (x^{16} y^{12}) - 8 \log (z)$

Rewrite $\log (x^{16} y^{12})$ as $\log (x^{16}) + \log (y^{12})$ .

$\log (x^{16}) + \log (y^{12}) - 8 \log (z)$

Expand $\log (x^{16})$ by moving $16$ outside the logarithm.

$16 \log (x) + \log (y^{12}) - 8 \log (z)$

Expand $\log (y^{12})$ by moving $12$ outside the logarithm.

$16 \log (x) + 12 \log (y) - 8 \log (z)$