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Popular >

simplify log_{243}(1/3)

Solution

simplify

lo g_{243} (\frac{1}{3})

Solution

- \frac{1}{5}

+1

Decimal Notation

- 0.2

Solution steps

lo g_{243} (\frac{1}{3})

Factor the number:

243 = 3^{5}

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

Apply log rule:

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

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

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

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

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

Apply log rule:

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

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

= \frac{1}{5} (- 1)

\frac{1}{5} (- 1) = - \frac{1}{5}

= - \frac{1}{5}

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Frequently Asked Questions (FAQ)

What is log_{243}(1/3) ?
The solution to log_{243}(1/3) is -1/5