What is 2log_{10}(x)+log_{10}(y)-3log_{10}(x+y) ?

The solution to 2log_{10}(x)+log_{10}(y)-3log_{10}(x+y) is log_{10}((x^2y)/((x+y)^3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2log_{10}(x)+log_{10}(y)-3log_{10}(x+y)

simplify

2 lo g_{10} (x) + lo g_{10} (y) - 3 lo g_{10} (x + y)

lo g_{10} (\frac{x ^{2} y}{( x + y ) ^{3}})

Solution steps

2 lo g_{10} (x) + lo g_{10} (y) - 3 lo g_{10} (x + y)

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

= lo g_{10} (x^{2}) + lo g_{10} (y) - 3 lo g_{10} (x + y)

Apply log rule:

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

lo g_{10} (x^{2}) + lo g_{10} (y) = lo g_{10} (x^{2} y)

= lo g_{10} (x^{2} y) - 3 lo g_{10} (x + y)

Apply log rule:

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

3 lo g_{10} (x + y) = lo g_{10} ((x + y)^{3})

= lo g_{10} (x^{2} y) - lo g_{10} ((x + y)^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x^{2} y) - lo g_{10} ((x + y)^{3}) = lo g_{10} (\frac{x ^{2} y}{( x + y ) ^{3}})

= lo g_{10} (\frac{x ^{2} y}{( x + y ) ^{3}})

\frac{1}{2} ln (x) + \frac{1}{2} ln (y) - \frac{1}{2} ln (z)

lo g_{5} (2 x (8 x + 7))

ln (ln (4)) - ln (ln (2))

lo g_{10} (y) + 11 lo g_{10} (z)

What is 2log_{10}(x)+log_{10}(y)-3log_{10}(x+y) ?
The solution to 2log_{10}(x)+log_{10}(y)-3log_{10}(x+y) is log_{10}((x^2y)/((x+y)^3))