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Popular >

simplify log_{4}(1/2)

Solution

simplify

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

Solution

- \frac{1}{2}

+1

Decimal Notation

- 0.5

Solution steps

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

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

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

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

Apply log rule:

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

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

= \frac{1}{2} (- 1)

\frac{1}{2} (- 1) = - \frac{1}{2}

= - \frac{1}{2}

Popular Examples

x^{2} = 4 x - 1

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6 a^{2} + ab - 15 b^{2}

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3 n^{6} - 33 n^{5} + 72 n^{4}

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\frac{2 m + 4}{m} \cdot \frac{m}{m + 2}

factor 10v^2+47v-15 factor

10 v^{2} + 47 v - 15

Frequently Asked Questions (FAQ)

What is log_{4}(1/2) ?
The solution to log_{4}(1/2) is -1/2