Algebra Examples

$\log (\sqrt[3]{7 x^{4}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7 x^{4}}$ as ${(7 x^{4})}^{\frac{1}{3}}$ .

$\log ({(7 x^{4})}^{\frac{1}{3}})$

Step 2

Expand $\log ({(7 x^{4})}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log (7 x^{4})$

Step 3

Rewrite $\log (7 x^{4})$ as $\log (7) + \log (x^{4})$ .

$\frac{1}{3} (\log (7) + \log (x^{4}))$

Step 4

Expand $\log (x^{4})$ by moving $4$ outside the logarithm.

$\frac{1}{3} (\log (7) + 4 \log (x))$

Step 5

Apply the distributive property.

$\frac{1}{3} \log (7) + \frac{1}{3} (4 \log (x))$

Step 6

Combine $\frac{1}{3}$ and $\log (7)$ .

$\frac{\log (7)}{3} + \frac{1}{3} (4 \log (x))$

Step 7

Multiply $\frac{1}{3} (4 \log (x))$ .

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Step 7.1

Combine $4$ and $\frac{1}{3}$ .

$\frac{\log (7)}{3} + \frac{4}{3} \log (x)$

Step 7.2

Combine $\frac{4}{3}$ and $\log (x)$ .

$\frac{\log (7)}{3} + \frac{4 \log (x)}{3}$