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Popular >

simplify log_{25}(0.008)

Solution

simplify

lo g_{25} (0.008)

Solution

- \frac{3}{2}

+1

Decimal Notation

- 1.5

Solution steps

lo g_{25} (0.008)

Factor the number:

25 = 5^{2}

= lo g_{5^{2}} (0.008)

Apply log rule:

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

lo g_{5^{2}} (0.008) = \frac{1}{2} lo g_{5} (0.008)

= \frac{1}{2} lo g_{5} (0.008)

0.008 = \frac{8}{1000}

= \frac{1}{2} lo g_{5} (\frac{8}{1000})

\frac{8}{1000} = 5^{- 3}

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

Apply log rule:

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

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

= \frac{1}{2} (- 3)

\frac{1}{2} (- 3) = - \frac{3}{2}

= - \frac{3}{2}

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Frequently Asked Questions (FAQ)

What is log_{25}(0.008) ?
The solution to log_{25}(0.008) is -3/2