Simplify/Condense

Problem

3*ln(x)+4*ln(y)−2*ln(z)

Solution

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

ln(x3)+ln(y4)−ln(z2)

2. Apply the product property of logarithms, which states ln(a)+ln(b)=ln(a*b) to the first two terms.

ln(x3*y4)−ln(z2)

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

ln((x3*y4)/(z2))

Final Answer

3*ln(x)+4*ln(y)−2*ln(z)=ln((x3*y4)/(z2))

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