Precalculus Examples

$\log_{7} (\frac{1}{z^{7}})$

Step 1

Rewrite $\log_{7} (\frac{1}{z^{7}})$ as $\log_{7} (1) - \log_{7} (z^{7})$ .

$\log_{7} (1) - \log_{7} (z^{7})$

Step 2

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

$\log_{7} (1) - (7 \log_{7} (z))$

Step 3

Logarithm base $7$ of $1$ is $0$ .

$0 - (7 \log_{7} (z))$

Step 4

Subtract $7 \log_{7} (z)$ from $0$ .

$- (7 \log_{7} (z))$

Step 5

Multiply $7$ by $- 1$ .

$- 7 \log_{7} (z)$