Precalculus Examples

$10 \log (\sqrt[3]{x})$

Step 1

Simplify $10 \log (\sqrt[3]{x})$ by moving $10$ inside the logarithm.

$\log ({\sqrt[3]{x}}^{10})$

Step 2

Rewrite ${\sqrt[3]{x}}^{10}$ as $\sqrt[3]{x^{10}}$ .

$\log (\sqrt[3]{x^{10}})$

Step 3

Rewrite $x^{10}$ as ${(x^{3})}^{3} x$ .

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Step 3.1

Factor out $x^{9}$ .

$\log (\sqrt[3]{x^{9} x})$

Step 3.2

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

Step 4

Pull terms out from under the radical.

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