Simplify/Condense 3 natural log of x+2 natural log of x+1

Problem

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

Solution

1. Apply the Power Property of logarithms, which states n*ln(a)=ln(a^n) to both terms in the expression.

ln(x^3)+ln((x+1)^2)

2. Apply the Product Property of logarithms, which states ln(a)+ln(b)=ln(a*b) to combine the two logarithmic terms into a single logarithm.

ln(x^3*(x+1)^2)

Final Answer

3*ln(x)+2*ln(x+1)=ln(x^3*(x+1)^2)

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