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Popular >

simplify log_{81}(1/27)

Solution

simplify

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

Solution

- \frac{3}{4}

+1

Solution steps

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

Factor the number:

81 = 3^{4}

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

Apply log rule:

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

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

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

\frac{1}{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} (- 3)

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

= - \frac{3}{4}

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3 x^{2} + 6 x - 45

- 23.2 = 6.1 x + 7.3

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- 3 x^{2} - 18 x

x^{4} (x - 7) \leq 0

factor 7u^2-28m^2 factor

7 u^{2} - 28 m^{2}

Frequently Asked Questions (FAQ)

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