What is log_{10}(10a)+log_{10}(10b) ?

The solution to log_{10}(10a)+log_{10}(10b) is 2+log_{10}(ab)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(10a)+log_{10}(10b)

simplify

lo g_{10} (10 a) + lo g_{10} (10 b)

2 + lo g_{10} (ab)

Solution steps

lo g_{10} (10 a) + lo g_{10} (10 b)

Apply log rule:

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

lo g_{10} (10 a) + lo g_{10} (10 b) = lo g_{10} (10 a \cdot 10 b)

= lo g_{10} (10 a \cdot 10 b)

Simplify

10 a \cdot 10 b : 100 ab

= lo g_{10} (100 ab)

Apply log rule:

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

lo g_{10} (100 ab) = lo g_{10} (100) + lo g_{10} (a) + lo g_{10} (b)

= lo g_{10} (100) + lo g_{10} (a) + lo g_{10} (b)

lo g_{10} (100) = 2

= 2 + lo g_{10} (a) + lo g_{10} (b)

Apply log rule:

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

lo g_{10} (a) + lo g_{10} (b) = lo g_{10} (ab)

= 2 + lo g_{10} (ab)

0.4 x 1 0^{- 8} 1 x 1 0^{- 1}

x^{3} + 4 x^{2} + x \cdot y^{2} + 4 y^{2}

(4 x y^{2})^{- 3}

(b) \cdot 52 \cdot (3 + 2) \cdot (5 + 2)

s^{- 2}

What is log_{10}(10a)+log_{10}(10b) ?
The solution to log_{10}(10a)+log_{10}(10b) is 2+log_{10}(ab)