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Popular >

simplify log_{16}(1/32)

Solution

simplify

lo g_{16} (\frac{1}{32})

Solution

- \frac{5}{4}

+1

Decimal Notation

- 1.25

Solution steps

lo g_{16} (\frac{1}{32})

Factor the number:

16 = 2^{4}

= lo g_{2^{4}} (\frac{1}{32})

Apply log rule:

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

lo g_{2^{4}} (\frac{1}{32}) = \frac{1}{4} lo g_{2} (\frac{1}{32})

= \frac{1}{4} lo g_{2} (\frac{1}{32})

\frac{1}{32} = 2^{- 5}

= \frac{1}{4} lo g_{2} (2^{- 5})

Apply log rule:

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

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

= \frac{1}{4} (- 5)

\frac{1}{4} (- 5) = - \frac{5}{4}

= - \frac{5}{4}

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Frequently Asked Questions (FAQ)

What is log_{16}(1/32) ?
The solution to log_{16}(1/32) is -5/4