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Popular >

simplify log_{125}(sqrt(5))

Solution

simplify

lo g_{125} (5)

Solution

\frac{1}{6}

+1

Decimal Notation

0.16666 \dots

Solution steps

lo g_{125} (5)

Factor the number:

125 = 5^{3}

= lo g_{5^{3}} (5)

Apply log rule:

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

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

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

Apply radical rule:

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

5 = 5^{\frac{1}{2}}

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

Apply log rule:

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

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

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

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

= \frac{1}{6}

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Frequently Asked Questions (FAQ)

What is log_{125}(sqrt(5)) ?
The solution to log_{125}(sqrt(5)) is 1/6