Precalculus Examples

$\log_{4} (\frac{39}{9})$

Step 1

Rewrite $\log_{4} (\frac{39}{9})$ as $\log_{4} (39) - \log_{4} (9)$ .

$\log_{4} (39) - \log_{4} (9)$

Step 2

Rewrite $\log_{4} (9)$ as $\log_{4} (3^{2})$ .

$\log_{4} (39) - \log_{4} (3^{2})$

Step 3

Expand $\log_{4} (3^{2})$ by moving $2$ outside the logarithm.

$\log_{4} (39) - (2 \log_{4} (3))$

Step 4

Multiply $2$ by $- 1$ .

$\log_{4} (39) - 2 \log_{4} (3)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\log_{4} (39)$ as $\log_{4} (3 (13))$ .

$\log_{4} (3 (13)) - 2 \log_{4} (3)$

Step 5.2

Rewrite $\log_{4} (3 (13))$ as $\log_{4} (3) + \log_{4} (13)$ .

$\log_{4} (3) + \log_{4} (13) - 2 \log_{4} (3)$

Step 6

Subtract $2 \log_{4} (3)$ from $\log_{4} (3)$ .

$\log_{4} (13) - \log_{4} (3)$