What is 2ln|x-2|-ln|x-3| ?

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

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simplify 2ln|x-2|-ln|x-3|

simplify

2 ln ∣ x - 2 ∣ - ln ∣ x - 3 ∣

ln (\frac{( x - 2 ) ^{2}}{∣ x - 3 ∣})

Solution steps

2 ln ∣ x - 2 ∣ - ln ∣ x - 3 ∣

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 - 3 ∣

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 ∣})

∣ x - 2 ∣^{2} = (x - 2)^{2}

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

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