en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

ln (x^{2} - 1)

Solution

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

Solution steps

ln (x^{2} - 1)

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

Popular Examples

f(x)=x^2e^{11x}

f (x) = x^{2} e^{11 x}

integral of (x^3)/(sqrt(x^4+1))

\int \frac{x ^{3}}{x ^{4} + 1} d x

limit as x approaches 0 of (tan(x))/(5x)

x \to 0 lim (\frac{tan ( x )}{5 x})

y^{'''}-6y^{''}+12y^'-8y=0

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

(e^xcos(y)+2x)dx-(e^xsin(y))dy=0

(e^{x} cos (y) + 2 x) d x - (e^{x} sin (y)) d y = 0

Frequently Asked Questions (FAQ)

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