Precalculus Examples

$10 \log_{4} (\sqrt[3]{y})$

Step 1

Simplify $10 \log_{4} (\sqrt[3]{y})$ by moving $10$ inside the logarithm.

$\log_{4} ({\sqrt[3]{y}}^{10})$

Step 2

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

$\log_{4} (\sqrt[3]{y^{10}})$

Step 3

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

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Step 3.1

Factor out $y^{9}$ .

$\log_{4} (\sqrt[3]{y^{9} y})$

Step 3.2

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

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

Step 4

Pull terms out from under the radical.

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