en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{128}(1/4)

Solution

simplify

lo g_{128} (\frac{1}{4})

Solution

- \frac{2}{7}

+1

Decimal Notation

- 0.28571 \dots

Solution steps

lo g_{128} (\frac{1}{4})

Factor the number:

128 = 2^{7}

= lo g_{2^{7}} (\frac{1}{4})

Apply log rule:

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

lo g_{2^{7}} (\frac{1}{4}) = \frac{1}{7} lo g_{2} (\frac{1}{4})

= \frac{1}{7} lo g_{2} (\frac{1}{4})

\frac{1}{4} = 2^{- 2}

= \frac{1}{7} lo g_{2} (2^{- 2})

Apply log rule:

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

lo g_{2} (2^{- 2}) = - 2

= \frac{1}{7} (- 2)

\frac{1}{7} (- 2) = - \frac{2}{7}

= - \frac{2}{7}

Popular Examples

simplify 38\times 2 simplify

38 \times 2

simplify 3/(x+2)+5/(x-4)simplify

\frac{3}{x + 2} + \frac{5}{x - 4}

simplify-4sqrt(-144)simplify

- 4 - 144

factor-5yz+10xz factor

- 5 yz + 10 x z

factor 6x^2-25x+4 factor

6 x^{2} - 25 x + 4

Frequently Asked Questions (FAQ)

What is log_{128}(1/4) ?
The solution to log_{128}(1/4) is -2/7