What is 1/3 (ln(y)-2ln(x+y)) ?

The solution to 1/3 (ln(y)-2ln(x+y)) is 1/3 ln(y/((x+y)^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/3 (ln(y)-2ln(x+y))

simplify

\frac{1}{3} (ln (y) - 2 ln (x + y))

\frac{1}{3} ln (\frac{y}{( x + y ) ^{2}})

Solution steps

\frac{1}{3} (ln (y) - 2 ln (x + y))

Apply log rule:

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

2 ln (y + x) = ln ((y + x)^{2})

= \frac{1}{3} (ln (y) - ln ((y + x)^{2}))

Apply log rule:

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

ln (y) - ln ((x + y)^{2}) = ln (\frac{y}{( y + x ) ^{2}})

= \frac{1}{3} ln (\frac{y}{( x + y ) ^{2}})

ln (1.5 a e^{b t})

lo g_{10} (x (x - 1)^{2})

2 x ln (3 x) - 4 x - 4 ln (3 x) + 8

ln (\frac{( a + b ) ^{2}}{c})

ln (ab) + ln (\frac{a}{b})

What is 1/3 (ln(y)-2ln(x+y)) ?
The solution to 1/3 (ln(y)-2ln(x+y)) is 1/3 ln(y/((x+y)^2))