Simplify/Condense 4 natural log of x-4 natural log of y

Problem

4*ln(x)−4*ln(y)

Solution

1. Factor out the common coefficient of 4 from both terms in the expression.

4*(ln(x)−ln(y))

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

4*ln(x/y)

3. Apply the power rule for logarithms, which states that n*ln(a)=ln(an) to move the coefficient into the exponent.

ln((x/y)4)

4. Distribute the exponent to both the numerator and the denominator inside the natural log.

ln((x4)/(y4))

Final Answer

4*ln(x)−4*ln(y)=ln((x4)/(y4))

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