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Popular >

simplify log_{243}(9)

Solution

simplify

lo g_{243} (9)

Solution

\frac{2}{5}

+1

Decimal Notation

0.4

Solution steps

lo g_{243} (9)

Factor the number:

243 = 3^{5}

= lo g_{3^{5}} (9)

Apply log rule:

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

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

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

Factor the number:

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} \cdot 2

\frac{1}{5} \cdot 2 = \frac{2}{5}

= \frac{2}{5}

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Frequently Asked Questions (FAQ)

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