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

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

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

simplify

ln ∣ 4 x + 1 ∣ - ln ∣ x + 1 ∣ + C

ln (\frac{∣ 4 x + 1 ∣}{∣ x + 1 ∣}) + C

Solution steps

ln ∣ 4 x + 1 ∣ - ln ∣ x + 1 ∣ + C

Apply log rule:

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

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

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

lo g_{10} (4) + lo g_{10} (9)

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ln (- 5 e^{x})

ln (x (x + 4) (x + 6))

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