Simplify/Condense

Problem

5*ln(x−2)−ln(x+2)−3*ln(x)

Solution

1. Apply the power property of logarithms, which states n*ln(a)=ln(an) to the first and third terms.

ln((x−2)5)−ln(x+2)−ln(x3)

2. Apply the quotient property of logarithms, which states ln(a)−ln(b)=ln(a/b) to the first two terms.

ln(((x−2)5)/(x+2))−ln(x3)

3. Apply the quotient property again to combine the remaining terms into a single logarithm.

ln(((x−2)5)/((x+2)*x3))

Final Answer

5*ln(x−2)−ln(x+2)−3*ln(x)=ln(((x−2)5)/(x3*(x+2)))

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