en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^2)/(1-x))

Solution

simplify

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

Solution

2 ln (x) - ln (1 - x)

Solution steps

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

Apply log rule:

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

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

= ln (x^{2}) - ln (- x + 1)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (x) - ln (1 - x)

Popular Examples

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

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

simplify ln((x-5)/(x-3))simplify

ln (\frac{x - 5}{x - 3})

simplify ln(csc(θ))+ln(tan(θ))simplify

ln (csc (θ)) + ln (tan (θ))

simplify ln(n^2+3)-ln(2n^2-1)simplify

ln (n^{2} + 3) - ln (2 n^{2} - 1)

simplify ln(-2)+ln(-5)simplify

ln (- 2) + ln (- 5)

Frequently Asked Questions (FAQ)

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