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Popular >

simplify log_{27}(1/3)

Solution

simplify

lo g_{27} (\frac{1}{3})

Solution

- \frac{1}{3}

+1

Decimal Notation

- 0.33333 \dots

Solution steps

lo g_{27} (\frac{1}{3})

Factor the number:

27 = 3^{3}

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

Apply log rule:

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

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

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

\frac{1}{3} = 3^{- 1}

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

Apply log rule:

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

lo g_{3} (3^{- 1}) = - 1

= \frac{1}{3} (- 1)

\frac{1}{3} (- 1) = - \frac{1}{3}

= - \frac{1}{3}

Popular Examples

factor 5x^2-13xy+8y^2 factor

5 x^{2} - 13 x y + 8 y^{2}

factor (x^2-4x-3)(x^2-4x+1)-12 factor

(x^{2} - 4 x - 3) (x^{2} - 4 x + 1) - 12

x^{2} - 2 x + 12 = 0

factor 9a^2-36a+32 factor

9 a^{2} - 36 a + 32

simplify (33!)/(6!(33-6)!)simplify

\frac{33 !}{6 ! ( 33 - 6 ) !}

Frequently Asked Questions (FAQ)

What is log_{27}(1/3) ?
The solution to log_{27}(1/3) is -1/3