What is log_{1/9}(3sqrt(3)) ?

The solution to log_{1/9}(3sqrt(3)) is -3/4

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simplify log_{1/9}(3sqrt(3))

simplify

lo g_{\frac{1}{9}} (33)

- \frac{3}{4}

Decimal

- 0.75

Solution steps

lo g_{\frac{1}{9}} (33)

Apply log rule:

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

lo g_{\frac{1}{9}} (33) = - lo g_{9} (33)

= - lo g_{9} (33)

Factor the number:

9 = 3^{2}

= - lo g_{3^{2}} (33)

Apply log rule:

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

lo g_{3^{2}} (33) = \frac{1}{2} lo g_{3} (33)

= - \frac{1}{2} lo g_{3} (33)

33 = 3^{\frac{3}{2}}

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

Apply log rule:

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

lo g_{3} (3^{\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}

2 x^{3} - 7 x^{2} - 19 x + 60

lo g_{12} (4)

x^{4} - 2 x^{3} - 21 x^{2} + 22 x + 40

f (a) = \frac{12 a ^{3} - 3 a}{12 a ^{3} + 6 a ^{2}}

(x^{2})^{3} + x^{2}