Trigonometry Examples

$\log_{2} ({(8 x)}^{\frac{1}{3}})$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $8 x$ .

$\log_{2} (8^{\frac{1}{3}} x^{\frac{1}{3}})$

Step 1.2

Rewrite $8$ as $2^{3}$ .

$\log_{2} ({(2^{3})}^{\frac{1}{3}} x^{\frac{1}{3}})$

Step 1.3

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

$\log_{2} (2^{3 (\frac{1}{3})} x^{\frac{1}{3}})$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\log_{2} (2^{3 (\frac{1}{3})} x^{\frac{1}{3}})$

Step 2.2

Rewrite the expression.

$\log_{2} (2^{1} x^{\frac{1}{3}})$

Step 3

Evaluate the exponent.

$\log_{2} (2 x^{\frac{1}{3}})$