Precalculus Examples

$5 \log_{4} (\frac{a^{2} b}{n^{3}})$

Step 1

Rewrite $\log_{4} (\frac{a^{2} b}{n^{3}})$ as $\log_{4} (a^{2} b) - \log_{4} (n^{3})$ .

$5 (\log_{4} (a^{2} b) - \log_{4} (n^{3}))$

Step 2

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

$5 (\log_{4} (a^{2} b) - (3 \log_{4} (n)))$

Step 3

Multiply $3$ by $- 1$ .

$5 (\log_{4} (a^{2} b) - 3 \log_{4} (n))$

Step 4

Rewrite $\log_{4} (a^{2} b)$ as $\log_{4} (a^{2}) + \log_{4} (b)$ .

$5 (\log_{4} (a^{2}) + \log_{4} (b) - 3 \log_{4} (n))$

Step 5

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

$5 (2 \log_{4} (a) + \log_{4} (b) - 3 \log_{4} (n))$

Step 6

Apply the distributive property.

$5 (2 \log_{4} (a)) + 5 \log_{4} (b) + 5 (- 3 \log_{4} (n))$

Step 7

Simplify.

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Step 7.1

Multiply $2$ by $5$ .

$10 \log_{4} (a) + 5 \log_{4} (b) + 5 (- 3 \log_{4} (n))$

Step 7.2

Multiply $- 3$ by $5$ .

$10 \log_{4} (a) + 5 \log_{4} (b) - 15 \log_{4} (n)$