What is x^2-13/6 ln|x+2|+19/6 ln|x-4|+4 ?

The solution to x^2-13/6 ln|x+2|+19/6 ln|x-4|+4 is x^2+ln(\sqrt[6]{(|x-4|^{19})/(|x+2|^{13)}})+4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify x^2-13/6 ln|x+2|+19/6 ln|x-4|+4

simplify

x^{2} - \frac{13}{6} ln ∣ x + 2 ∣ + \frac{19}{6} ln ∣ x - 4 ∣ + 4

Solution steps

x^{2} - \frac{13}{6} ln ∣ x + 2 ∣ + \frac{19}{6} ln ∣ x - 4 ∣ + 4

Apply log rule:

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

\frac{13}{6} ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{\frac{13}{6}})

= x^{2} - ln (∣ x + 2 ∣^{\frac{13}{6}}) + \frac{19}{6} ln ∣ x - 4 ∣ + 4

Apply log rule:

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

\frac{19}{6} ln ∣ x - 4 ∣ = ln (∣ x - 4 ∣^{\frac{19}{6}})

= x^{2} - ln (∣ x + 2 ∣^{\frac{13}{6}}) + ln (∣ x - 4 ∣^{\frac{19}{6}}) + 4

Apply log rule:

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

ln (∣ x - 4 ∣^{\frac{19}{6}}) - ln (∣ x + 2 ∣^{\frac{13}{6}}) = ln (\frac{∣ x - 4 ∣ ^{\frac{19}{6}}}{∣ x + 2 ∣ ^{\frac{13}{6}}})

= x^{2} + ln (\frac{∣ x - 4 ∣ ^{\frac{19}{6}}}{∣ x + 2 ∣ ^{\frac{13}{6}}}) + 4

Combine same powers :

9 \cdot ln (3) - ln (2!) + 7 \cdot ln (2) - ln (7!) - 3 \cdot 3

ln (a + b) + 4 ln (a - b) - 5 ln (C)

12 lo g_{10} (x) + 5 lo g_{10} (y)

ln (\frac{1}{e ^{x} + 1})

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

What is x^2-13/6 ln|x+2|+19/6 ln|x-4|+4 ?
The solution to x^2-13/6 ln|x+2|+19/6 ln|x-4|+4 is x^2+ln(\sqrt[6]{(|x-4|^{19})/(|x+2|^{13)}})+4