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Popular >

simplify log_{27}(1/9)

Solution

simplify

lo g_{27} (\frac{1}{9})

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

lo g_{27} (\frac{1}{9})

Factor the number:

27 = 3^{3}

= lo g_{3^{3}} (\frac{1}{9})

Apply log rule:

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

lo g_{3^{3}} (\frac{1}{9}) = \frac{1}{3} lo g_{3} (\frac{1}{9})

= \frac{1}{3} lo g_{3} (\frac{1}{9})

\frac{1}{9} = 3^{- 2}

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

Apply log rule:

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

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

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

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

= - \frac{2}{3}

Popular Examples

factor x^3+3x^2-3x-9 factor

x^{3} + 3 x^{2} - 3 x - 9

\frac{2}{3} \leq - 9

-1/3 x+5/6 x+2=-1/2+1/6 x

- \frac{1}{3} x + \frac{5}{6} x + 2 = - \frac{1}{2} + \frac{1}{6} x

25 = (y - 8)^{2}

simplify 3^{log_{3}(4)}simplify

3^{l o g_{3} (4)}

Frequently Asked Questions (FAQ)

What is log_{27}(1/9) ?
The solution to log_{27}(1/9) is -2/3