What is simplify-ln|x-1|+1/(x-1)+ln|x-2| ?

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

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simplify-ln|x-1|+1/(x-1)+ln|x-2|

simplify

- ln ∣ x - 1 ∣ + \frac{1}{x - 1} + ln ∣ x - 2 ∣

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

Solution steps

- ln ∣ x - 1 ∣ + \frac{1}{x - 1} + ln ∣ x - 2 ∣

Apply log rule:

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

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

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

lo g_{3} (3 x^{2})

2 lo g_{5} (6) - \frac{1}{2} lo g_{5} (4)

\frac{1}{5} lo g_{10} (mn) + lo g_{10} (m^{2} n) - \frac{1}{10} lo g_{10} (mn)

ln (\frac{x ^{2}}{y ^{3}})

ln (x^{2} - y^{2}) - ln (x - y)

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