en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(4000)

Solution

simplify

lo g_{10} (4000)

Solution

3 + 2 lo g_{10} (2)

+1

Decimal Notation

3.60205 \dots

Solution steps

lo g_{10} (4000)

Factor the number:

4000 = 1 0^{3} \cdot 4

= lo g_{10} (1 0^{3} \cdot 4)

Apply log rule:

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

lo g_{10} (1 0^{3} \cdot 4) = lo g_{10} (1 0^{3}) + lo g_{10} (4)

= lo g_{10} (1 0^{3}) + lo g_{10} (4)

Apply log rule:

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

lo g_{10} (1 0^{3}) = 3

= 3 + lo g_{10} (4)

lo g_{10} (4) = 2 lo g_{10} (2)

= 3 + 2 lo g_{10} (2)

Popular Examples

expand (3x^2+4x-7)(x-2)expand

(3 x^{2} + 4 x - 7) (x - 2)

simplify sqrt(144a^{10)}simplify

144 a^{10}

simplify ((-15x^2-8y^2+22xy))/((2y-3x))simplify

\frac{( - 15 x ^{2} - 8 y ^{2} + 22 x y )}{( 2 y - 3 x )}

simplify 1/(sqrt(2))*2 simplify

\frac{1}{2} \cdot 2

simplify cos^2(x)tan^2(x)simplify

cos^{2} (x) tan^{2} (x)

Frequently Asked Questions (FAQ)

What is log_{10}(4000) ?
The solution to log_{10}(4000) is 3+2log_{10}(2)