Expand the Logarithmic Expression natural log of 6/( square root of x^2+1)

Problem

ln(6/√(,x2+1))

Solution

1. Apply the quotient rule for logarithms, which states that ln(a/b)=ln(a)−ln(b)

ln(6/√(,x2+1))=ln(6)−ln(√(,x2+1))

2. Rewrite the radical using an exponent. The square root of an expression is equivalent to that expression raised to the power of 1/2

ln(6)−ln(√(,x2+1))=ln(6)−ln((x2+1)(1/2))

3. Apply the power rule for logarithms, which states that ln(an)=n*ln(a) to move the exponent in front of the natural log.

ln(6)−ln((x2+1)(1/2))=ln(6)−1/2*ln(x2+1)

Final Answer

ln(6/√(,x2+1))=ln(6)−1/2*ln(x2+1)

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