en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{8}(1/16)

Solution

simplify

lo g_{8} (\frac{1}{16})

Solution

- \frac{4}{3}

+1

Solution steps

lo g_{8} (\frac{1}{16})

Factor the number:

8 = 2^{3}

= lo g_{2^{3}} (\frac{1}{16})

Apply log rule:

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

lo g_{2^{3}} (\frac{1}{16}) = \frac{1}{3} lo g_{2} (\frac{1}{16})

= \frac{1}{3} lo g_{2} (\frac{1}{16})

\frac{1}{16} = 2^{- 4}

= \frac{1}{3} lo g_{2} (2^{- 4})

Apply log rule:

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

lo g_{2} (2^{- 4}) = - 4

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

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

= - \frac{4}{3}

Popular Examples

simplify-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)simplify

- 2 x (x^{3} - 6 x^{2} + 6) + 4 x^{3} - (5 x^{4} + 10 x)

expand-mnp(3m-5n+7p)expand

- mn p (3 m - 5 n + 7 p)

factor 4x^3+2x^2-14x+3 factor

4 x^{3} + 2 x^{2} - 14 x + 3

expand (n+2)*(0.5n+1)expand

(n + 2) \cdot (0.5 n + 1)

simplify (4-x^2)^2-(x+2)^2 simplify

(4 - x^{2})^{2} - (x + 2)^{2}

Frequently Asked Questions (FAQ)

What is log_{8}(1/16) ?
The solution to log_{8}(1/16) is -4/3