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Popular >

simplify log_{8}(0.5)

Solution

simplify

lo g_{8} (0.5)

Solution

- \frac{1}{3}

+1

Decimal Notation

- 0.33333 \dots

Solution steps

lo g_{8} (0.5)

Factor the number:

8 = 2^{3}

= lo g_{2^{3}} (0.5)

Apply log rule:

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

lo g_{2^{3}} (0.5) = \frac{1}{3} lo g_{2} (0.5)

= \frac{1}{3} lo g_{2} (0.5)

0.5 = \frac{5}{10}

= \frac{1}{3} lo g_{2} (\frac{5}{10})

\frac{5}{10} = 2^{- 1}

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

Apply log rule:

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

lo g_{2} (2^{- 1}) = - 1

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

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

= - \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is log_{8}(0.5) ?
The solution to log_{8}(0.5) is -1/3