Simplify/Condense natural log of z(z-1)^2

Problem

ln(z*(z−1)2)

Solution

1. Identify the expression as a natural logarithm of a product of two terms: z and (z−1)2

2. Apply the product rule for logarithms, which states that ln(a*b)=ln(a)+ln(b)

3. Expand the expression using this rule to separate the terms.

ln(z*(z−1)2)=ln(z)+ln((z−1)2)

4. Apply the power rule for logarithms, which states that ln(an)=n*ln(a) to the second term.

ln(z)+ln((z−1)2)=ln(z)+2*ln(z−1)

Final Answer

ln(z*(z−1)2)=ln(z)+2*ln(z−1)

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