Evaluate natural log of ((x+1)^2)/((x-1)^4)

Problem

ln(((x+1)2)/((x−1)4))

Solution

1. Apply the quotient rule for logarithms, which states that ln(a/b)=ln(a)−ln(b)

ln(((x+1)2)/((x−1)4))=ln((x+1)2)−ln((x−1)4)

2. Apply the power rule for logarithms, which states that ln(an)=n*ln(a) to both terms.

ln((x+1)2)=2*ln(x+1)

ln((x−1)4)=4*ln(x−1)

3. Combine the results to express the simplified logarithmic form.

2*ln(x+1)−4*ln(x−1)

Final Answer

ln(((x+1)2)/((x−1)4))=2*ln(x+1)−4*ln(x−1)

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