Simplify/Condense 1/2* natural log of x- natural log of 3

Problem

1/2*ln(x)−ln(3)

Solution

1. Apply the power property of logarithms, which states that a*ln(b)=ln(ba) to the first term.

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

2. Rewrite the exponent as a radical, noting that x(1/2)=√(,x)

ln(x(1/2))=ln(√(,x))

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

ln(√(,x))−ln(3)=ln(√(,x)/3)

Final Answer

1/2*ln(x)−ln(3)=ln(√(,x)/3)

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