Precalculus Examples

$\log_{7} (\frac{31}{10})$

Step 1

Rewrite $\log_{7} (\frac{31}{10})$ as $\log_{7} (31) - \log_{7} (10)$ .

$\log_{7} (31) - \log_{7} (10)$

Step 2

Rewrite $\log_{7} (10)$ as $\log_{7} (2 (5))$ .

$\log_{7} (31) - \log_{7} (2 (5))$

Step 3

Rewrite $\log_{7} (2 (5))$ as $\log_{7} (2) + \log_{7} (5)$ .

$\log_{7} (31) - (\log_{7} (2) + \log_{7} (5))$

Step 4

Apply the distributive property.

$\log_{7} (31) - \log_{7} (2) - \log_{7} (5)$