Simplify/Condense

Problem

ln(3)−2*ln(4)+ln(32)

Solution

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

ln(3)−ln(4)+ln(32)

2. Evaluate the exponent inside the natural log.

ln(3)−ln(16)+ln(32)

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

ln(3/16)+ln(32)

4. Apply the product property of logarithms, which states ln(a)+ln(b)=ln(a⋅b)

ln(3/16⋅32)

5. Simplify the expression inside the natural log by performing the multiplication.

ln(3⋅2)

ln(6)

Final Answer

ln(3)−2*ln(4)+ln(32)=ln(6)

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