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Popular >

simplify log_{8}(0.125)

Solution

simplify

lo g_{8} (0.125)

Solution

- 1

Solution steps

lo g_{8} (0.125)

Factor the number:

8 = 2^{3}

= lo g_{2^{3}} (0.125)

Apply log rule:

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

lo g_{2^{3}} (0.125) = \frac{1}{3} lo g_{2} (0.125)

= \frac{1}{3} lo g_{2} (0.125)

0.125 = \frac{125}{1000}

= \frac{1}{3} lo g_{2} (\frac{125}{1000})

\frac{125}{1000} = 2^{- 3}

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

Apply log rule:

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

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

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

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

= - 1

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Frequently Asked Questions (FAQ)

What is log_{8}(0.125) ?
The solution to log_{8}(0.125) is -1