Simplify/Condense 11 natural log of x-2-3 natural log of x

Problem

11*ln(x−2)−3*ln(x)

Solution

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

ln((x−2)11)−ln(x3)

2. Apply the Quotient Property of logarithms, which states ln(a)−ln(b)=ln(a/b) to combine the two terms into a single logarithm.

ln(((x−2)11)/(x3))

Final Answer

11*ln(x−2)−3*ln(x)=ln(((x−2)11)/(x3))

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