Precalculus Examples

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

Step 1

Simplify $9 \log (\sqrt[3]{x})$ by moving $9$ inside the logarithm.

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

Step 2

Rewrite ${\sqrt[3]{x}}^{9}$ as $x^{3}$ .

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Step 2.1

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

$\log ({(x^{\frac{1}{3}})}^{9})$

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (x^{\frac{1}{3} \cdot 9})$

Step 2.3

Combine $\frac{1}{3}$ and $9$ .

$\log (x^{\frac{9}{3}})$

Step 2.4

Cancel the common factor of $9$ and $3$ .

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Step 2.4.1

Factor $3$ out of $9$ .

$\log (x^{\frac{3 \cdot 3}{3}})$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $3$ out of $3$ .

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

Step 2.4.2.2

Cancel the common factor.

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

Step 2.4.2.3

Rewrite the expression.

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

Step 2.4.2.4

Divide $3$ by $1$ .

$\log (x^{3})$