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Popular >

simplify log_{81}(27)

Solution

simplify

lo g_{81} (27)

Solution

\frac{3}{4}

+1

Decimal Notation

0.75

Solution steps

lo g_{81} (27)

Factor the number:

81 = 3^{4}

= lo g_{3^{4}} (27)

Apply log rule:

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

lo g_{3^{4}} (27) = \frac{1}{4} lo g_{3} (27)

= \frac{1}{4} lo g_{3} (27)

Factor the number:

27 = 3^{3}

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

Apply log rule:

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

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

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

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

= \frac{3}{4}

Popular Examples

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simplify (x^{-12/5}*y^{-3/16}*2^{4/3})^{5/6}simplify

(x^{- \frac{12}{5}} \cdot y^{- \frac{3}{16}} \cdot 2^{\frac{4}{3}})^{\frac{5}{6}}

7 = \frac{4}{3} (x + 6)

Frequently Asked Questions (FAQ)

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