Simplify/Condense

Problem

ln(a+b)+ln(a−b)−5*ln(c)

Solution

1. Apply the product rule for logarithms to the first two terms, which states that ln(x)+ln(y)=ln(x*y)

ln(a+b)+ln(a−b)=ln((a+b)*(a−b))

2. Simplify the product inside the logarithm using the difference of squares formula.

ln((a+b)*(a−b))=ln(a2−b2)

3. Apply the power rule for logarithms to the third term, which states that n*ln(x)=ln(xn)

5*ln(c)=ln(c5)

4. Apply the quotient rule for logarithms to combine the remaining terms, which states that ln(x)−ln(y)=ln(x/y)

ln(a2−b2)−ln(c5)=ln((a2−b2)/(c5))

Final Answer

ln(a+b)+ln(a−b)−5*ln(c)=ln((a2−b2)/(c5))

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