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Popular >

simplify log_{16}(1/128)

Solution

simplify

lo g_{16} (\frac{1}{128})

Solution

- \frac{7}{4}

+1

Decimal Notation

- 1.75

Solution steps

lo g_{16} (\frac{1}{128})

Factor the number:

16 = 2^{4}

= lo g_{2^{4}} (\frac{1}{128})

Apply log rule:

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

lo g_{2^{4}} (\frac{1}{128}) = \frac{1}{4} lo g_{2} (\frac{1}{128})

= \frac{1}{4} lo g_{2} (\frac{1}{128})

\frac{1}{128} = 2^{- 7}

= \frac{1}{4} lo g_{2} (2^{- 7})

Apply log rule:

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

lo g_{2} (2^{- 7}) = - 7

= \frac{1}{4} (- 7)

\frac{1}{4} (- 7) = - \frac{7}{4}

= - \frac{7}{4}

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Frequently Asked Questions (FAQ)

What is log_{16}(1/128) ?
The solution to log_{16}(1/128) is -7/4