Expand the Logarithmic Expression

Problem

ln(√(,(x4)/(y3)))

Solution

1. Rewrite the radical as a fractional exponent using the property √(,a)=a(1/2)

ln(((x4)/(y3))(1/2))

2. Apply the power rule for logarithms, ln(ak)=k*ln(a) to move the exponent to the front.

1/2*ln((x4)/(y3))

3. Apply the quotient rule for logarithms, ln(a/b)=ln(a)−ln(b) to separate the numerator and denominator.

1/2*(ln(x4)−ln(y3))

4. Apply the power rule again to the individual terms inside the parentheses.

1/2*(4*ln(x)−3*ln(y))

5. Distribute the constant factor to simplify the expression.

2*ln(x)−3/2*ln(y)

Final Answer

ln(√(,(x4)/(y3)))=2*ln(x)−3/2*ln(y)

Want more problems? Check here!