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Popular >

simplify log_{16}(sqrt(2))

Solution

simplify

lo g_{16} (2)

Solution

\frac{1}{8}

+1

Decimal Notation

0.125

Solution steps

lo g_{16} (2)

Factor the number:

16 = 2^{4}

= lo g_{2^{4}} (2)

Apply log rule:

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

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

2 = 2^{\frac{1}{2}}

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

Apply log rule:

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

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

= \frac{1}{4} \cdot \frac{1}{2}

\frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8}

= \frac{1}{8}

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Frequently Asked Questions (FAQ)

What is log_{16}(sqrt(2)) ?
The solution to log_{16}(sqrt(2)) is 1/8