Precalculus Examples

$\log_{8} (\frac{1}{z^{9}})$

Step 1

Rewrite $\log_{8} (\frac{1}{z^{9}})$ as $\log_{8} (1) - \log_{8} (z^{9})$ .

$\log_{8} (1) - \log_{8} (z^{9})$

Step 2

Expand $\log_{8} (z^{9})$ by moving $9$ outside the logarithm.

$\log_{8} (1) - (9 \log_{8} (z))$

Step 3

Logarithm base $8$ of $1$ is $0$ .

$0 - (9 \log_{8} (z))$

Step 4

Subtract $9 \log_{8} (z)$ from $0$ .

$- (9 \log_{8} (z))$

Step 5

Multiply $9$ by $- 1$ .

$- 9 \log_{8} (z)$