Precalculus Examples

$\log_{8} (\frac{39}{2})$

Step 1

Rewrite $\log_{8} (\frac{39}{2})$ as $\log_{8} (39) - \log_{8} (2)$ .

$\log_{8} (39) - \log_{8} (2)$

Step 2

Logarithm base $8$ of $2$ is $\frac{1}{3}$ .

$\log_{8} (39) - \frac{1}{3}$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{8} (39)$ as $\log_{8} (3 (13))$ .

$\log_{8} (3 (13)) - \frac{1}{3}$

Step 3.2

Rewrite $\log_{8} (3 (13))$ as $\log_{8} (3) + \log_{8} (13)$ .

$\log_{8} (3) + \log_{8} (13) - \frac{1}{3}$