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Popular >

simplify log_{81}(3)

Solution

simplify

lo g_{81} (3)

Solution

\frac{1}{4}

+1

Solution steps

lo g_{81} (3)

Factor the number:

81 = 3^{4}

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{3} (3) = 1

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

Multiply the numbers:

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

= \frac{1}{4}

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Frequently Asked Questions (FAQ)

What is log_{81}(3) ?
The solution to log_{81}(3) is 1/4