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Popular >

simplify log_{216}(6)

Solution

simplify

lo g_{216} (6)

Solution

\frac{1}{3}

+1

Decimal Notation

0.33333 \dots

Solution steps

lo g_{216} (6)

Factor the number:

216 = 6^{3}

= lo g_{6^{3}} (6)

Apply log rule:

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

lo g_{6^{3}} (6) = \frac{1}{3} lo g_{6} (6)

= \frac{1}{3} lo g_{6} (6)

Apply log rule:

lo g_{a} (a) = 1

lo g_{6} (6) = 1

= \frac{1}{3} \cdot 1

Multiply the numbers:

\frac{1}{3} \cdot 1 = \frac{1}{3}

= \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is log_{216}(6) ?
The solution to log_{216}(6) is 1/3