What is log_{\sqrt[5]{27}}((sqrt(3))/(81)) ?

The solution to log_{\sqrt[5]{27}}((sqrt(3))/(81)) is -35/6

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simplify log_{\sqrt[5]{27}}((sqrt(3))/(81))

simplify

- \frac{35}{6}

Solution steps

Factor

= lo g_{3^{\frac{3}{5}}} (\frac{3}{81})

Apply log rule:

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

lo g_{3^{\frac{3}{5}}} (\frac{3}{81}) = \frac{1}{\frac{3}{5}} lo g_{3} (\frac{3}{81})

= \frac{1}{\frac{3}{5}} lo g_{3} (\frac{3}{81})

Cancel

\frac{3}{81} : \frac{1}{3 \cdot 27}

= \frac{1}{\frac{3}{5}} lo g_{3} (\frac{1}{3 \cdot 27})

\frac{1}{3 \cdot 27} = 3^{- \frac{7}{2}}

= \frac{1}{\frac{3}{5}} lo g_{3} (3^{- \frac{7}{2}})

Apply log rule:

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

lo g_{3} (3^{- \frac{7}{2}}) = - \frac{7}{2}

= \frac{1}{\frac{3}{5}} (- \frac{7}{2})

\frac{1}{\frac{3}{5}} (- \frac{7}{2}) = - \frac{35}{6}

= - \frac{35}{6}

- 5 m - 3 n + 6 + 2 m + 2 n - 8

(\frac{3}{- 3})^{4}

\frac{1}{9} \cdot \frac{2}{3}

1 \frac{4}{11}

5432

What is log_{\sqrt[5]{27}}((sqrt(3))/(81)) ?
The solution to log_{\sqrt[5]{27}}((sqrt(3))/(81)) is -35/6