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Popular >

simplify log_{243}(1/9)

Solution

simplify

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

Solution

- \frac{2}{5}

+1

Decimal Notation

- 0.4

Solution steps

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

Factor the number:

243 = 3^{5}

= lo g_{3^{5}} (\frac{1}{9})

Apply log rule:

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

lo g_{3^{5}} (\frac{1}{9}) = \frac{1}{5} lo g_{3} (\frac{1}{9})

= \frac{1}{5} lo g_{3} (\frac{1}{9})

\frac{1}{9} = 3^{- 2}

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

Apply log rule:

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

lo g_{3} (3^{- 2}) = - 2

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

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

= - \frac{2}{5}

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(1 + i)^{- 2}

2 x - 9 = 2 x - 9

longdivision (a2+11a+24)/(a3+27)long division

\frac{a 2 + 11 a + 24}{a 3 + 27}

Frequently Asked Questions (FAQ)

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