en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{4}(1/32)

Solution

simplify

lo g_{4} (\frac{1}{32})

Solution

- \frac{5}{2}

+1

Decimal Notation

- 2.5

Solution steps

lo g_{4} (\frac{1}{32})

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (\frac{1}{32})

Apply log rule:

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

lo g_{2^{2}} (\frac{1}{32}) = \frac{1}{2} lo g_{2} (\frac{1}{32})

= \frac{1}{2} lo g_{2} (\frac{1}{32})

\frac{1}{32} = 2^{- 5}

= \frac{1}{2} lo g_{2} (2^{- 5})

Apply log rule:

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

lo g_{2} (2^{- 5}) = - 5

= \frac{1}{2} (- 5)

\frac{1}{2} (- 5) = - \frac{5}{2}

= - \frac{5}{2}

Popular Examples

simplify (25a^3b^7)/(-15a^8b^3)simplify

\frac{25 a ^{3} b ^{7}}{- 15 a ^{8} b ^{3}}

simplify sqrt(5)-2.25 simplify

5 - 2.25

3 x^{2} - 21 x = 0

1936 - 16 t^{2} = 0

factor 2x^2+x-6 factor

2 x^{2} + x - 6

Frequently Asked Questions (FAQ)

What is log_{4}(1/32) ?
The solution to log_{4}(1/32) is -5/2