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Popular >

simplify log_{243}(81)

Solution

simplify

lo g_{243} (81)

Solution

\frac{4}{5}

+1

Decimal Notation

0.8

Solution steps

lo g_{243} (81)

Factor the number:

243 = 3^{5}

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

Apply log rule:

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

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

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

Factor the number:

81 = 3^{4}

= \frac{1}{5} lo g_{3} (3^{4})

Apply log rule:

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

lo g_{3} (3^{4}) = 4

= \frac{1}{5} \cdot 4

\frac{1}{5} \cdot 4 = \frac{4}{5}

= \frac{4}{5}

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Frequently Asked Questions (FAQ)

What is log_{243}(81) ?
The solution to log_{243}(81) is 4/5