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Popular >

simplify log_{36}(1/6)

Solution

simplify

lo g_{36} (\frac{1}{6})

Solution

- \frac{1}{2}

+1

Decimal Notation

- 0.5

Solution steps

lo g_{36} (\frac{1}{6})

Factor the number:

36 = 6^{2}

= lo g_{6^{2}} (\frac{1}{6})

Apply log rule:

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

lo g_{6^{2}} (\frac{1}{6}) = \frac{1}{2} lo g_{6} (\frac{1}{6})

= \frac{1}{2} lo g_{6} (\frac{1}{6})

\frac{1}{6} = 6^{- 1}

= \frac{1}{2} lo g_{6} (6^{- 1})

Apply log rule:

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

lo g_{6} (6^{- 1}) = - 1

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

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

= - \frac{1}{2}

Popular Examples

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\frac{48 x ^{3}}{3 x y ^{2}}

3 = y + 6

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3 x^{2} + 10 x + 7

factor sqrt(x^3)factor

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2 w^{2} - 15 w + 19 = 0

Frequently Asked Questions (FAQ)

What is log_{36}(1/6) ?
The solution to log_{36}(1/6) is -1/2