What is 4ln|x-1|+6ln|x|-1/x+C ?

The solution to 4ln|x-1|+6ln|x|-1/x+C is ln(x^6(x-1)^4)-1/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4ln|x-1|+6ln|x|-1/x+C

simplify

4 ln ∣ x - 1 ∣ + 6 ln ∣ x ∣ - \frac{1}{x} + C

ln (x^{6} (x - 1)^{4}) - \frac{1}{x} + C

Solution steps

4 ln ∣ x - 1 ∣ + 6 ln ∣ x ∣ - \frac{1}{x} + C

Apply log rule:

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

4 ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{4})

= ln (∣ x - 1 ∣^{4}) + 6 ln ∣ x ∣ - \frac{1}{x} + C

Apply log rule:

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

6 ln ∣ x ∣ = ln (∣ x ∣^{6})

= ln (∣ x - 1 ∣^{4}) + ln (∣ x ∣^{6}) - \frac{1}{x} + C

Apply log rule:

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

ln (∣ x - 1 ∣^{4}) + ln (∣ x ∣^{6}) = ln (∣ x ∣^{6} ∣ x - 1 ∣^{4})

= ln (∣ x ∣^{6} ∣ x - 1 ∣^{4}) - \frac{1}{x} + C

Simplify

∣ x - 1 ∣^{4} ∣ x ∣^{6} : x^{6} (x - 1)^{4}

= ln (x^{6} (x - 1)^{4}) - \frac{1}{x} + C

4 lo g_{10} (x) - \frac{1}{3} lo g_{10} (x + 6)

9 ln (\frac{9}{2})

4 lo g_{10} (x) + lo g_{10} (y) - 3 lo g_{10} (w)

lo g_{10} (\frac{4 ^{7} - 9 ^{4}}{6 ^{5}})

ln (\frac{e ^{2 x}}{x})

What is 4ln|x-1|+6ln|x|-1/x+C ?
The solution to 4ln|x-1|+6ln|x|-1/x+C is ln(x^6(x-1)^4)-1/x+C