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Popular >

simplify log_{sqrt(3)}(1/81)

Solution

simplify

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

Solution

- 8

Solution steps

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

Apply radical rule:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

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

Apply log rule:

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

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

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

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

= \frac{1}{\frac{1}{2}} lo g_{3} (3^{- 4})

Apply log rule:

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

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

= \frac{1}{\frac{1}{2}} (- 4)

\frac{1}{\frac{1}{2}} (- 4) = - 8

= - 8

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Frequently Asked Questions (FAQ)

What is log_{sqrt(3)}(1/81) ?
The solution to log_{sqrt(3)}(1/81) is -8