en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{2}(4000)

Solution

simplify

lo g_{2} (4000)

Solution

5 + 3 lo g_{2} (5)

+1

Solution steps

lo g_{2} (4000)

Factor the number:

4000 = 2^{5} \cdot 125

= lo g_{2} (2^{5} \cdot 125)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (2^{5} \cdot 125) = lo g_{2} (2^{5}) + lo g_{2} (125)

= lo g_{2} (2^{5}) + lo g_{2} (125)

Apply log rule:

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

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

= 5 + lo g_{2} (125)

lo g_{2} (125) = 3 lo g_{2} (5)

= 5 + 3 lo g_{2} (5)

Popular Examples

simplify (20v^9)/((4v)^2)simplify

\frac{20 v ^{9}}{( 4 v ) ^{2}}

simplify (3x)/(2x-6)+9/(6-2x)simplify

\frac{3 x}{2 x - 6} + \frac{9}{6 - 2 x}

factor-x^3+x factor

- x^{3} + x

factor 8q^4t+2q^3t^2-6q^2t^4 factor

8 q^{4} t + 2 q^{3} t^{2} - 6 q^{2} t^{4}

simplify log_{sqrt(5)}(25sqrt(5))simplify

lo g_{5} (255)

Frequently Asked Questions (FAQ)

What is log_{2}(4000) ?
The solution to log_{2}(4000) is 5+3log_{2}(5)