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Popular >

simplify log_{100}(sqrt(10))

Solution

simplify

lo g_{100} (10)

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

lo g_{100} (10)

Factor the number:

100 = 1 0^{2}

= lo g_{1 0^{2}} (10)

Apply log rule:

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

lo g_{1 0^{2}} (10) = \frac{1}{2} lo g_{10} (10)

= \frac{1}{2} lo g_{10} (10)

Apply radical rule:

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

10 = 1 0^{\frac{1}{2}}

= \frac{1}{2} lo g_{10} (1 0^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (1 0^{\frac{1}{2}}) = \frac{1}{2}

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

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

= \frac{1}{4}

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Frequently Asked Questions (FAQ)

What is log_{100}(sqrt(10)) ?
The solution to log_{100}(sqrt(10)) is 1/4