Expand the Logarithmic Expression natural log of xyz^2

Problem

ln(x*y*z2)

Solution

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

ln(x*y*z2)=ln(x)+ln(y)+ln(z2)

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

ln(z2)=2*ln(z)

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

ln(x)+ln(y)+2*ln(z)

Final Answer

ln(x*y*z2)=ln(x)+ln(y)+2*ln(z)

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