Expand the Logarithmic Expression natural log of z(z-1)^2

Problem

ln(z*(z−1)2)

Solution

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

ln(z*(z−1)2)=ln(z)+ln((z−1)2)

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

ln((z−1)2)=2*ln(z−1)

3. Combine the terms to write the fully expanded expression.

ln(z)+2*ln(z−1)

Final Answer

ln(z*(z−1)2)=ln(z)+2*ln(z−1)

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