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Popular >

simplify log_{128}(1/64)

Solution

simplify

lo g_{128} (\frac{1}{64})

Solution

- \frac{6}{7}

+1

Decimal Notation

- 0.85714 \dots

Solution steps

lo g_{128} (\frac{1}{64})

Factor the number:

128 = 2^{7}

= lo g_{2^{7}} (\frac{1}{64})

Apply log rule:

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

lo g_{2^{7}} (\frac{1}{64}) = \frac{1}{7} lo g_{2} (\frac{1}{64})

= \frac{1}{7} lo g_{2} (\frac{1}{64})

\frac{1}{64} = 2^{- 6}

= \frac{1}{7} lo g_{2} (2^{- 6})

Apply log rule:

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

lo g_{2} (2^{- 6}) = - 6

= \frac{1}{7} (- 6)

\frac{1}{7} (- 6) = - \frac{6}{7}

= - \frac{6}{7}

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Frequently Asked Questions (FAQ)

What is log_{128}(1/64) ?
The solution to log_{128}(1/64) is -6/7