Precalculus Examples

$\log ({(\frac{1}{5})}^{5})$

Step 1

Expand $\log ({(\frac{1}{5})}^{5})$ by moving $5$ outside the logarithm.

$5 \log (\frac{1}{5})$

Step 2

Rewrite $\log (\frac{1}{5})$ as $\log (1) - \log (5)$ .

$5 (\log (1) - \log (5))$

Step 3

Logarithm base $10$ of $1$ is $0$ .

$5 (0 - \log (5))$

Step 4

Subtract $\log (5)$ from $0$ .

$5 (- \log (5))$

Step 5

Multiply $- 1$ by $5$ .

$- 5 \log (5)$