Precalculus Examples

$\log_{5} (\frac{3}{8})$

Step 1

Rewrite $\log_{5} (\frac{3}{8})$ as $\log_{5} (3) - \log_{5} (8)$ .

$\log_{5} (3) - \log_{5} (8)$

Step 2

Rewrite $\log_{5} (8)$ as $\log_{5} (2^{3})$ .

$\log_{5} (3) - \log_{5} (2^{3})$

Step 3

Expand $\log_{5} (2^{3})$ by moving $3$ outside the logarithm.

$\log_{5} (3) - (3 \log_{5} (2))$

Step 4

Multiply $3$ by $- 1$ .

$\log_{5} (3) - 3 \log_{5} (2)$