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Popular >

simplify log_{27}(1/81)

Solution

simplify

lo g_{27} (\frac{1}{81})

Solution

- \frac{4}{3}

+1

Decimal Notation

- 1.33333 \dots

Solution steps

lo g_{27} (\frac{1}{81})

Factor the number:

27 = 3^{3}

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

Apply log rule:

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

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

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

\frac{1}{81} = 3^{- 4}

= \frac{1}{3} lo g_{3} (3^{- 4})

Apply log rule:

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

lo g_{3} (3^{- 4}) = - 4

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

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

= - \frac{4}{3}

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Frequently Asked Questions (FAQ)

What is log_{27}(1/81) ?
The solution to log_{27}(1/81) is -4/3