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

\frac{ln ( \frac{3}{2} ) ln ( \frac{8}{7} )}{ln ( \frac{7}{6} )} + ln (\frac{1}{2})

\frac{1}{3} ln (\frac{11}{5})

20000 - \frac{1}{4 ln ( 2 )}

0.9 \cdot lo g_{2} (0.9) + 0.1 \cdot lo g_{2} (0.1)

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