Precalculus Examples

$\log_{5} (\frac{x}{6})$

Step 1

Rewrite $\log_{5} (\frac{x}{6})$ as $\log_{5} (x) - \log_{5} (6)$ .

$\log_{5} (x) - \log_{5} (6)$

Step 2

Rewrite $\log_{5} (6)$ as $\log_{5} (2 (3))$ .

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

Step 3

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

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

Step 4

Apply the distributive property.

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