en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{81}(1/27)

Solution

simplify

lo g_{81} (\frac{1}{27})

Solution

- \frac{3}{4}

+1

Decimal Notation

- 0.75

Solution steps

lo g_{81} (\frac{1}{27})

Factor the number:

81 = 3^{4}

= lo g_{3^{4}} (\frac{1}{27})

Apply log rule:

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

lo g_{3^{4}} (\frac{1}{27}) = \frac{1}{4} lo g_{3} (\frac{1}{27})

= \frac{1}{4} lo g_{3} (\frac{1}{27})

\frac{1}{27} = 3^{- 3}

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

Apply log rule:

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

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

= \frac{1}{4} (- 3)

\frac{1}{4} (- 3) = - \frac{3}{4}

= - \frac{3}{4}

Popular Examples

factor 3x^2+6x-45 factor

3 x^{2} + 6 x - 45

- 23.2 = 6.1 x + 7.3

factor-3x^2-18x factor

- 3 x^{2} - 18 x

simplify 1+(0.07)/(12)simplify

1 + \frac{0.07}{12}

x^{4} (x - 7) \leq 0

Frequently Asked Questions (FAQ)

What is log_{81}(1/27) ?
The solution to log_{81}(1/27) is -3/4