Precalculus Examples

$\log (\frac{x^{8} z}{y^{2}})$

Step 1

Rewrite $\log (\frac{x^{8} z}{y^{2}})$ as $\log (x^{8} z) - \log (y^{2})$ .

$\log (x^{8} z) - \log (y^{2})$

Step 2

Expand $\log (y^{2})$ by moving $2$ outside the logarithm.

$\log (x^{8} z) - (2 \log (y))$

Step 3

Multiply $2$ by $- 1$ .

$\log (x^{8} z) - 2 \log (y)$

Step 4

Rewrite $\log (x^{8} z)$ as $\log (x^{8}) + \log (z)$ .

$\log (x^{8}) + \log (z) - 2 \log (y)$

Step 5

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

$8 \log (x) + \log (z) - 2 \log (y)$