Precalculus Examples

$\log_{4} ({(\frac{5^{3}}{11})}^{3})$

Step 1

Expand $\log_{4} ({(\frac{5^{3}}{11})}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{4} (\frac{5^{3}}{11})$

Step 2

Raise $5$ to the power of $3$ .

$3 \log_{4} (\frac{125}{11})$

Step 3

Rewrite $\log_{4} (\frac{125}{11})$ as $\log_{4} (125) - \log_{4} (11)$ .

$3 (\log_{4} (125) - \log_{4} (11))$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{4} (125)$ as $\log_{4} (5^{3})$ .

$3 (\log_{4} (5^{3}) - \log_{4} (11))$

Step 4.2

Expand $\log_{4} (5^{3})$ by moving $3$ outside the logarithm.

$3 (3 \log_{4} (5) - \log_{4} (11))$

Step 5

Apply the distributive property.

$3 (3 \log_{4} (5)) + 3 (- \log_{4} (11))$

Step 6

Multiply $3$ by $3$ .

$9 \log_{4} (5) + 3 (- \log_{4} (11))$

Step 7

Multiply $- 1$ by $3$ .

$9 \log_{4} (5) - 3 \log_{4} (11)$