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Popular >

simplify log_{9}(1/243)

Solution

simplify

lo g_{9} (\frac{1}{243})

Solution

- \frac{5}{2}

+1

Decimal Notation

- 2.5

Solution steps

lo g_{9} (\frac{1}{243})

Factor the number:

9 = 3^{2}

= lo g_{3^{2}} (\frac{1}{243})

Apply log rule:

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

lo g_{3^{2}} (\frac{1}{243}) = \frac{1}{2} lo g_{3} (\frac{1}{243})

= \frac{1}{2} lo g_{3} (\frac{1}{243})

\frac{1}{243} = 3^{- 5}

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

Apply log rule:

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

lo g_{3} (3^{- 5}) = - 5

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

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

= - \frac{5}{2}

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Frequently Asked Questions (FAQ)

What is log_{9}(1/243) ?
The solution to log_{9}(1/243) is -5/2