What is 2ln|x+2|-ln|x-4|+C ?

The solution to 2ln|x+2|-ln|x-4|+C is ln(((x+2)^2)/(|x-4|))+C

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simplify 2ln|x+2|-ln|x-4|+C

simplify

2 ln ∣ x + 2 ∣ - ln ∣ x - 4 ∣ + C

ln (\frac{( x + 2 ) ^{2}}{∣ x - 4 ∣}) + C

Solution steps

2 ln ∣ x + 2 ∣ - ln ∣ x - 4 ∣ + C

Apply log rule:

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

2 ln ∣ x + 2 ∣ = ln (∣ x + 2 ∣^{2})

= ln (∣ x + 2 ∣^{2}) - ln ∣ x - 4 ∣ + C

Apply log rule:

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

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

= ln (\frac{∣ x + 2 ∣ ^{2}}{∣ x - 4 ∣}) + C

∣ x + 2 ∣^{2} = (x + 2)^{2}

= ln (\frac{( x + 2 ) ^{2}}{∣ x - 4 ∣}) + C

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What is 2ln|x+2|-ln|x-4|+C ?
The solution to 2ln|x+2|-ln|x-4|+C is ln(((x+2)^2)/(|x-4|))+C