What is log_{3}(9/(mn)) ?

The solution to log_{3}(9/(mn)) is 2-log_{3}(m)-log_{3}(n)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{3}(9/(mn))

simplify

lo g_{3} (\frac{9}{mn})

2 - lo g_{3} (m) - lo g_{3} (n)

Solution steps

lo g_{3} (\frac{9}{mn})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{9}{mn}) = lo g_{3} (9) - lo g_{3} (mn)

= lo g_{3} (9) - lo g_{3} (mn)

lo g_{3} (9) = 2

lo g_{3} (mn) = lo g_{3} (m) + lo g_{3} (n)

= 2 - (lo g_{3} (m) + lo g_{3} (n))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{3} (m) + lo g_{3} (n)) = - lo g_{3} (m) - lo g_{3} (n)

= 2 - lo g_{3} (m) - lo g_{3} (n)

lo g_{3} (5 x^{3})

3 lo g_{b} (z) + lo g_{b} (y) - 4 lo g_{b} (z)

ln (4 e^{5 x})

ln (\frac{6}{17})

- lo g_{10} (5.1 \cdot 1 0^{- 4})

What is log_{3}(9/(mn)) ?
The solution to log_{3}(9/(mn)) is 2-log_{3}(m)-log_{3}(n)