Simplify/Condense

Problem

ln(2)+ln(6)−1/2*ln(9)

Solution

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

1/2*ln(9)=ln(9(1/2))

2. Simplify the exponent by calculating the square root of 9.

ln(9(1/2))=ln(3)

3. Apply the product property of logarithms to the first two terms, which states ln(a)+ln(b)=ln(a*b)

ln(2)+ln(6)=ln(2⋅6)

ln(2⋅6)=ln(12)

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

ln(12)−ln(3)=ln(12/3)

5. Simplify the fraction inside the natural logarithm.

ln(12/3)=ln(4)

Final Answer

ln(2)+ln(6)−1/2*ln(9)=ln(4)

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