What is log_{1/4}(2sqrt(2)) ?

The solution to log_{1/4}(2sqrt(2)) is -3/4

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simplify log_{1/4}(2sqrt(2))

simplify

lo g_{\frac{1}{4}} (22)

- \frac{3}{4}

Decimal Notation

- 0.75

Solution steps

lo g_{\frac{1}{4}} (22)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

lo g_{\frac{1}{4}} (22) = - lo g_{4} (22)

= - lo g_{4} (22)

Factor the number:

4 = 2^{2}

= - lo g_{2^{2}} (22)

Apply log rule:

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

lo g_{2^{2}} (22) = \frac{1}{2} lo g_{2} (22)

= - \frac{1}{2} lo g_{2} (22)

22 = 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} \cdot \frac{3}{2}

\frac{1}{2} \cdot \frac{3}{2} = \frac{3}{4}

= - \frac{3}{4}

\frac{1}{( s ^{3} + s ) s - 4}

12 - 75 + 147

(3 u - 1) (u + 2) + 7 u (u + 1)

\frac{( \frac{25}{a} - a )}{5 + a}

108 x^{6} + 27 x^{6}