Precalculus Examples

$\log_{4} (\frac{1}{9})$

Step 1

Rewrite $\log_{4} (\frac{1}{9})$ as $\log_{4} (1) - \log_{4} (9)$ .

$\log_{4} (1) - \log_{4} (9)$

Step 2

Logarithm base $4$ of $1$ is $0$ .

$0 - \log_{4} (9)$

Step 3

Rewrite $\log_{4} (9)$ as $\log_{4} (3^{2})$ .

$0 - \log_{4} (3^{2})$

Step 4

Expand $\log_{4} (3^{2})$ by moving $2$ outside the logarithm.

$0 - (2 \log_{4} (3))$

Step 5

Multiply $2$ by $- 1$ .

$0 - 2 \log_{4} (3)$

Step 6

Subtract $2 \log_{4} (3)$ from $0$ .

$- 2 \log_{4} (3)$