Precalculus Examples

$\frac{\log (5)}{\log (\frac{1}{3})}$

Step 1

Rewrite $\log (\frac{1}{3})$ as $\log (1) - \log (3)$ .

$\frac{\log (5)}{\log (1) - \log (3)}$

Step 2

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

$\frac{\log (5)}{0 - \log (3)}$

Step 3

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

$\frac{\log (5)}{- \log (3)}$

Step 4

Move the negative in front of the fraction.

$- \frac{\log (5)}{\log (3)}$