Precalculus Examples

$\log (\frac{\frac{1}{9}}{x})$

Step 1

Rewrite $\log (\frac{\frac{1}{9}}{x})$ as $\log (\frac{1}{9}) - \log (x)$ .

$\log (\frac{1}{9}) - \log (x)$

Step 2

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

$\log (1) - \log (9) - \log (x)$

Step 3

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

$0 - \log (9) - \log (x)$

Step 4

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

$0 - \log (3^{2}) - \log (x)$

Step 5

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

$0 - (2 \log (3)) - \log (x)$

Step 6

Multiply $2$ by $- 1$ .

$0 - 2 \log (3) - \log (x)$

Step 7

Subtract $2 \log (3)$ from $0$ .

$- 2 \log (3) - \log (x)$