en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(5000)

Solution

simplify

lo g_{10} (5000)

Solution

3 + lo g_{10} (5)

+1

Decimal Notation

3.69897 \dots

Solution steps

lo g_{10} (5000)

Factor the number:

5000 = 1 0^{3} \cdot 5

= lo g_{10} (1 0^{3} \cdot 5)

Apply log rule:

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

lo g_{10} (1 0^{3} \cdot 5) = lo g_{10} (1 0^{3}) + lo g_{10} (5)

= lo g_{10} (1 0^{3}) + lo g_{10} (5)

Apply log rule:

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

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

= 3 + lo g_{10} (5)

Popular Examples

simplify-15/9+1/24 simplify

- \frac{15}{9} + \frac{1}{24}

simplify sqrt(3-2)simplify

3 - 2

expand (4x-1)(2x-3)expand

(4 x - 1) (2 x - 3)

simplify (3x^4-6x^2-x)/x simplify

\frac{3 x ^{4} - 6 x ^{2} - x}{x}

simplify 1/(10^4)simplify

\frac{1}{1 0 ^{4}}

Frequently Asked Questions (FAQ)

What is log_{10}(5000) ?
The solution to log_{10}(5000) is 3+log_{10}(5)