What is 1/2 ln|x-2|+1/2 ln|x+2| ?

The solution to 1/2 ln|x-2|+1/2 ln|x+2| is ln(|x-2|^{1/2}|x+2|^{1/2})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 ln|x-2|+1/2 ln|x+2|

simplify

\frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x + 2 ∣

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

Solution steps

\frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x + 2 ∣

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{x ^{2} y}{4 e ^{5} y ^{3}})

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

\frac{1}{0.04} ln (\frac{72}{72 - 42})

ln (\frac{y ^{x} \cdot e ^{- y}}{x !})

ln (\frac{4 x + 1}{3 x - 1})

What is 1/2 ln|x-2|+1/2 ln|x+2| ?
The solution to 1/2 ln|x-2|+1/2 ln|x+2| is ln(|x-2|^{1/2}|x+2|^{1/2})