en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{243}(1/27)

Solution

simplify

lo g_{243} (\frac{1}{27})

Solution

- \frac{3}{5}

+1

Decimal Notation

- 0.6

Solution steps

lo g_{243} (\frac{1}{27})

Factor the number:

243 = 3^{5}

= lo g_{3^{5}} (\frac{1}{27})

Apply log rule:

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

lo g_{3^{5}} (\frac{1}{27}) = \frac{1}{5} lo g_{3} (\frac{1}{27})

= \frac{1}{5} lo g_{3} (\frac{1}{27})

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

= \frac{1}{5} lo g_{3} (3^{- 3})

Apply log rule:

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

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

= \frac{1}{5} (- 3)

\frac{1}{5} (- 3) = - \frac{3}{5}

= - \frac{3}{5}

Popular Examples

factor x+xy factor

x + x y

factor-2x^2+3x factor

- 2 x^{2} + 3 x

simplify 3/5-4 simplify

\frac{3}{5} - 4

simplify 10\times 1/2 simplify

10 \times \frac{1}{2}

simplify 5x+7-(2x)/(x-5)simplify

5 x + 7 - \frac{2 x}{x - 5}

Frequently Asked Questions (FAQ)

What is log_{243}(1/27) ?
The solution to log_{243}(1/27) is -3/5