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Popular >

simplify log_{8}(\sqrt[4]{2})

Solution

simplify

Solution

\frac{1}{12}

+1

Decimal Notation

0.08333 \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

Apply radical rule:

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

Apply log rule:

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

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

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

\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}

= \frac{1}{12}

Popular Examples

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\frac{csc ^{2} ( θ )}{cot ^{2} ( θ )}

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simplify 64-16(0.8-1)^2 simplify

64 - 16 (0.8 - 1)^{2}

Frequently Asked Questions (FAQ)

What is log_{8}(\sqrt[4]{2}) ?
The solution to log_{8}(\sqrt[4]{2}) is 1/12