What is ln(|x-1|^2)-ln|x-1| ?

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

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simplify ln(|x-1|^2)-ln|x-1|

simplify

ln (∣ x - 1 ∣^{2}) - ln ∣ x - 1 ∣

ln (\frac{( x - 1 ) ^{2}}{∣ x - 1 ∣})

Solution steps

ln (∣ x - 1 ∣^{2}) - ln ∣ x - 1 ∣

Apply log rule:

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

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

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

∣ x - 1 ∣^{2} = (x - 1)^{2}

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

ln ((\frac{1}{5})^{l n (x)})

5 lo g_{9} (x) + 7 lo g_{9} (y) - 3 lo g_{9} (z)

- 3 ln (x + 2) + 4 ln (x + 3)

- 4 (ln (4 - v) - ln (4 - u)) + 4 (ln (v) - ln (u))

ln (x + 1) + ln (x^{2} + 1)

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