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Popular >

simplify log_{9}(27/81)

Solution

simplify

lo g_{9} (\frac{27}{81})

Solution

- \frac{1}{2}

+1

Decimal Notation

- 0.5

Solution steps

lo g_{9} (\frac{27}{81})

Factor the number:

9 = 3^{2}

= lo g_{3^{2}} (\frac{27}{81})

Apply log rule:

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

lo g_{3^{2}} (\frac{27}{81}) = \frac{1}{2} lo g_{3} (\frac{27}{81})

= \frac{1}{2} lo g_{3} (\frac{27}{81})

\frac{27}{81} = 3^{- 1}

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

Apply log rule:

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

lo g_{3} (3^{- 1}) = - 1

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

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

= - \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is log_{9}(27/81) ?
The solution to log_{9}(27/81) is -1/2