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Popular >

simplify log_{81}(1/3)

Solution

simplify

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

Solution

- \frac{1}{4}

+1

Decimal Notation

- 0.25

Solution steps

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

Factor the number:

81 = 3^{4}

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

Apply log rule:

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

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

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

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

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

Apply log rule:

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

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

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

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

= - \frac{1}{4}

Popular Examples

-11<= 3x+4<= 22

- 11 \leq 3 x + 4 \leq 22

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simplify 3*(1/2)simplify

3 \cdot (\frac{1}{2})

∣ x + 3 ∣ \leq ∣ x ∣

Frequently Asked Questions (FAQ)

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