What is log_{4}(1/(sqrt(8))) ?

The solution to log_{4}(1/(sqrt(8))) is -3/4

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simplify log_{4}(1/(sqrt(8)))

simplify

lo g_{4} (\frac{1}{8})

- \frac{3}{4}

Solution steps

lo g_{4} (\frac{1}{8})

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (\frac{1}{8})

Apply log rule:

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

lo g_{2^{2}} (\frac{1}{8}) = \frac{1}{2} lo g_{2} (\frac{1}{8})

= \frac{1}{2} lo g_{2} (\frac{1}{8})

\frac{1}{8} = 2^{- \frac{3}{2}}

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

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

= - \frac{3}{4}

\frac{2}{( s - 2 ) ^{2} + 4} - \frac{1}{s - 2}

\frac{5 x ^{4} y ^{5}}{- 6 x ^{4} y}

\frac{1}{4} \cdot (- 4)

\frac{x}{3} + \frac{x}{2}

(3^{3})^{- 2}