en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{5}(200)

Solution

simplify

lo g_{5} (200)

Solution

2 + 3 lo g_{5} (2)

+1

Solution steps

lo g_{5} (200)

Factor the number:

200 = 5^{2} \cdot 8

= lo g_{5} (5^{2} \cdot 8)

Apply log rule:

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

lo g_{5} (5^{2} \cdot 8) = lo g_{5} (5^{2}) + lo g_{5} (8)

= lo g_{5} (5^{2}) + lo g_{5} (8)

Apply log rule:

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

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

= 2 + lo g_{5} (8)

lo g_{5} (8) = 3 lo g_{5} (2)

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

Popular Examples

simplify (5/(3r-1)-5)/(5/(3r-1)+5)simplify

\frac{\frac{5}{3 r - 1} - 5}{\frac{5}{3 r - 1} + 5}

simplify 35/45 simplify

\frac{35}{45}

simplify 4x^{-4}*1/2 x^2 simplify

4 x^{- 4} \cdot \frac{1}{2} x^{2}

expand (x+1)(x-3)^2 expand

(x + 1) (x - 3)^{2}

factor a(2+x)-(2+x)factor

a (2 + x) - (2 + x)

Frequently Asked Questions (FAQ)

What is log_{5}(200) ?
The solution to log_{5}(200) is 2+3log_{5}(2)