Simplify/Condense

Problem

2*ln(x)−1/2*ln(x+5)

Solution

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

ln(x2)−ln((x+5)(1/2))

2. Rewrite the exponent of 1/2 as a square root to simplify the notation.

ln(x2)−ln(√(,x+5))

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

ln((x2)/√(,x+5))

Final Answer

2*ln(x)−1/2*ln(x+5)=ln((x2)/√(,x+5))

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