What is simplify-ln|x-3|+2ln|x-2|+C ?

The solution to simplify-ln|x-3|+2ln|x-2|+C is ln(((x-2)^2)/(|x-3|))+C

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simplify-ln|x-3|+2ln|x-2|+C

simplify

- ln ∣ x - 3 ∣ + 2 ln ∣ x - 2 ∣ + C

ln (\frac{( x - 2 ) ^{2}}{∣ x - 3 ∣}) + C

Solution steps

- ln ∣ x - 3 ∣ + 2 ln ∣ x - 2 ∣ + C

Apply log rule:

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

2 ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{2})

= - ln ∣ x - 3 ∣ + ln (∣ x - 2 ∣^{2}) + C

Apply log rule:

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

ln (∣ x - 2 ∣^{2}) - ln ∣ x - 3 ∣ = ln (\frac{∣ x - 2 ∣ ^{2}}{∣ x - 3 ∣})

= ln (\frac{∣ x - 2 ∣ ^{2}}{∣ x - 3 ∣}) + C

∣ x - 2 ∣^{2} = (x - 2)^{2}

= ln (\frac{( x - 2 ) ^{2}}{∣ x - 3 ∣}) + C

ln (\frac{x ^{4}}{y ^{5}})

\frac{1}{2} ln (4 + 15)

ln (\frac{- 4.92}{4.79526})

e^{- 2} - ln (\frac{3}{7})

ln (\frac{x y ^{2}}{z ^{4}})

What is simplify-ln|x-3|+2ln|x-2|+C ?
The solution to simplify-ln|x-3|+2ln|x-2|+C is ln(((x-2)^2)/(|x-3|))+C