Expand the Logarithmic Expression natural log of (3x^2)/((x+1)^10)

Problem

ln((3*x2)/((x+1)10))

Solution

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

ln(3*x2)−ln((x+1)10)

2. Apply the product rule for logarithms to the first term, which states ln(a*b)=ln(a)+ln(b)

ln(3)+ln(x2)−ln((x+1)10)

3. Apply the power rule for logarithms to the remaining terms, which states ln(an)=n*ln(a)

ln(3)+2*ln(x)−10*ln(x+1)

Final Answer

ln((3*x2)/((x+1)10))=ln(3)+2*ln(x)−10*ln(x+1)

Want more problems? Check here!