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

The solution to ln(x+1)+1/2 ln(2+3((y-1)/(x+1))^2) is ln(sqrt(2x^2+4x+3y^2+5-6y))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

ln (2 x^{2} + 4 x + 3 y^{2} + 5 - 6 y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

(x + 1) (2 + 3 (\frac{y - 1}{x + 1})^{2})^{\frac{1}{2}} : 2 x^{2} + 4 x + 3 y^{2} + 5 - 6 y

= ln (2 x^{2} + 4 x + 3 y^{2} + 5 - 6 y)

lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}})

(\frac{1}{2})^{2} - \frac{1}{2} - ln (\frac{1}{2})

ln (\frac{16384 x ^{12} + 4}{0.1})

ln (0.023) - ln (0.02)

- lo g_{10} (\frac{1 0 ^{- 14}}{\frac{1}{30}})

What is ln(x+1)+1/2 ln(2+3((y-1)/(x+1))^2) ?
The solution to ln(x+1)+1/2 ln(2+3((y-1)/(x+1))^2) is ln(sqrt(2x^2+4x+3y^2+5-6y))