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Popular >

simplify log_{8}(sqrt(32))

Solution

simplify

lo g_{8} (32)

Solution

\frac{5}{6}

+1

Decimal Notation

0.83333 \dots

Solution steps

lo g_{8} (32)

Factor the number:

8 = 2^{3}

= lo g_{2^{3}} (32)

Apply log rule:

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

lo g_{2^{3}} (32) = \frac{1}{3} lo g_{2} (32)

= \frac{1}{3} lo g_{2} (32)

32 = 2^{\frac{5}{2}}

= \frac{1}{3} lo g_{2} (2^{\frac{5}{2}})

Apply log rule:

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

lo g_{2} (2^{\frac{5}{2}}) = \frac{5}{2}

= \frac{1}{3} \cdot \frac{5}{2}

\frac{1}{3} \cdot \frac{5}{2} = \frac{5}{6}

= \frac{5}{6}

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Frequently Asked Questions (FAQ)

What is log_{8}(sqrt(32)) ?
The solution to log_{8}(sqrt(32)) is 5/6