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Popular >

simplify 1/2 log_{25}(5)

Solution

simplify

\frac{1}{2} lo g_{25} (5)

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

\frac{1}{2} lo g_{25} (5)

Factor the number:

25 = 5^{2}

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{5} (5) = 1

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

Multiply the numbers:

\frac{1}{2} \cdot 1 = \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 1/2 log_{25}(5) ?
The solution to 1/2 log_{25}(5) is 1/4