What is simplify-ln|x|+5ln|x-1| ?

The solution to simplify-ln|x|+5ln|x-1| is ln((|x-1|^5)/(|x|))

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simplify-ln|x|+5ln|x-1|

simplify

- ln ∣ x ∣ + 5 ln ∣ x - 1 ∣

ln (\frac{∣ x - 1 ∣ ^{5}}{∣ x ∣})

Solution steps

- ln ∣ x ∣ + 5 ln ∣ x - 1 ∣

Apply log rule:

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

5 ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{5})

= - ln ∣ x ∣ + ln (∣ x - 1 ∣^{5})

Apply log rule:

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

ln (∣ x - 1 ∣^{5}) - ln ∣ x ∣ = ln (\frac{∣ x - 1 ∣ ^{5}}{∣ x ∣})

= ln (\frac{∣ x - 1 ∣ ^{5}}{∣ x ∣})

ln (\infty) - ln (- \infty)

ln (\frac{20}{35})

ln (\frac{( x + 2 ) ^{4} y \frac{1}{3}}{( w - 1 ) ^{3}})

9 ln (7) - 9 ln (5)

What is simplify-ln|x|+5ln|x-1| ?
The solution to simplify-ln|x|+5ln|x-1| is ln((|x-1|^5)/(|x|))