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Popular >

simplify log_{8}(\sqrt[3]{16})

Solution

simplify

Solution

\frac{4}{9}

+1

Decimal Notation

0.44444 \dots

Solution steps

Factor the number:

8 = 2^{3}

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

= \frac{1}{3} lo g_{2} (2^{\frac{4}{3}})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{2} (2^{\frac{4}{3}}) = \frac{4}{3}

= \frac{1}{3} \cdot \frac{4}{3}

\frac{1}{3} \cdot \frac{4}{3} = \frac{4}{9}

= \frac{4}{9}

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Frequently Asked Questions (FAQ)

What is log_{8}(\sqrt[3]{16}) ?
The solution to log_{8}(\sqrt[3]{16}) is 4/9