Precalculus Examples

$\log_{4} (7^{3} \sqrt[3]{2})$

Step 1

Rewrite $\log_{4} (7^{3} \sqrt[3]{2})$ as $\log_{4} (7^{3}) + \log_{4} (\sqrt[3]{2})$ .

$\log_{4} (7^{3}) + \log_{4} (\sqrt[3]{2})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

$\log_{4} (7^{3}) + \log_{4} (2^{\frac{1}{3}})$

Step 3

Expand $\log_{4} (7^{3})$ by moving $3$ outside the logarithm.

$3 \log_{4} (7) + \log_{4} (2^{\frac{1}{3}})$

Step 4

Expand $\log_{4} (2^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$3 \log_{4} (7) + \frac{1}{3} \log_{4} (2)$

Step 5

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$3 \log_{4} (7) + \frac{1}{3} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{1}{3} \cdot \frac{1}{2}$ .

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Step 6.1

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$3 \log_{4} (7) + \frac{1}{3 \cdot 2}$

Step 6.2

Multiply $3$ by $2$ .

$3 \log_{4} (7) + \frac{1}{6}$