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

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

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

simplify

2 ln ∣ x - 1 ∣ - ln ∣ x + 2 ∣ + C

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

Solution steps

2 ln ∣ x - 1 ∣ - ln ∣ x + 2 ∣ + C

Apply log rule:

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

2 ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{2})

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

Apply log rule:

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

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

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

∣ x - 1 ∣^{2} = (x - 1)^{2}

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

- lo g_{10} (2.1 \cdot 1 0^{- 53})

ln (1.6296 \cdot π)

lo g_{e} (6 x^{2} - 2) - lo g_{e} (x^{2})

\frac{1}{3} ln (2 x + 1) + \frac{1}{2} [ln (x - 4) - ln (x^{2} + 5)]

- lo g_{10} (5 (1 0^{- 2}))

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