What is simplify-ln(|x|^3)+ln(|x-1|^5)+c ?

The solution to simplify-ln(|x|^3)+ln(|x-1|^5)+c is ln((|x-1|^5)/(|x|^3))+c

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-ln(|x|^3)+ln(|x-1|^5)+c

simplify

- ln (∣ x ∣^{3}) + ln (∣ x - 1 ∣^{5}) + c

ln (\frac{∣ x - 1 ∣ ^{5}}{∣ x ∣ ^{3}}) + c

Solution steps

- ln (∣ x ∣^{3}) + ln (∣ x - 1 ∣^{5}) + c

Apply log rule:

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

ln (∣ x - 1 ∣^{5}) - ln (∣ x ∣^{3}) = ln (\frac{∣ x - 1 ∣ ^{5}}{∣ x ∣ ^{3}})

= ln (\frac{∣ x - 1 ∣ ^{5}}{∣ x ∣ ^{3}}) + c

- ln (\frac{1 - a}{a})

\frac{1}{2} ln (\frac{1 + \frac{3}{2}}{1 - \frac{3}{2}})

2 lo g_{10} (2 x + 3) + \frac{1}{2} lo g_{10} (x + 1)

2 ln (e^{8} + 5) - 2 ln (e^{6} + 5)

ln (\frac{1 - 0.04}{10 - 0.04})

What is simplify-ln(|x|^3)+ln(|x-1|^5)+c ?
The solution to simplify-ln(|x|^3)+ln(|x-1|^5)+c is ln((|x-1|^5)/(|x|^3))+c