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Popular >

simplify log_{64}((sqrt(2))/4)

Solution

simplify

lo g_{64} (\frac{2}{4})

Solution

- \frac{1}{4}

+1

Decimal Notation

- 0.25

Solution steps

lo g_{64} (\frac{2}{4})

Factor the number:

64 = 2^{6}

= lo g_{2^{6}} (\frac{2}{4})

Apply log rule:

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

lo g_{2^{6}} (\frac{2}{4}) = \frac{1}{6} lo g_{2} (\frac{2}{4})

= \frac{1}{6} lo g_{2} (\frac{2}{4})

Cancel

\frac{2}{4} : \frac{1}{2 \cdot 2}

= \frac{1}{6} lo g_{2} (\frac{1}{2 \cdot 2})

\frac{1}{2 \cdot 2} = 2^{- \frac{3}{2}}

= \frac{1}{6} lo g_{2} (2^{- \frac{3}{2}})

Apply log rule:

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

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

= \frac{1}{6} (- \frac{3}{2})

\frac{1}{6} (- \frac{3}{2}) = - \frac{1}{4}

= - \frac{1}{4}

Popular Examples

simplify-12/4 simplify

- \frac{12}{4}

4x+2(x-3)=4x+2x-11

4 x + 2 (x - 3) = 4 x + 2 x - 11

simplify (5^{-2})/(5^{-5)}simplify

\frac{5 ^{- 2}}{5 ^{- 5}}

5 - 3 n \geq - 4

5 x - 29 > - 34

Frequently Asked Questions (FAQ)

What is log_{64}((sqrt(2))/4) ?
The solution to log_{64}((sqrt(2))/4) is -1/4