Simplify/Condense 2 log of x-6 log of x-9

Problem

2*(log_)(x)−6*(log_)(x−9)

Solution

1. Identify the logarithmic properties needed to condense the expression, specifically the Power Property and the Quotient Property.

2. Apply the Power Property, which states n*(log_)(a)=(log_)(an) to move the coefficients into the exponents of the arguments.

2*(log_)(x)=(log_)(x2)

6*(log_)(x−9)=(log_)((x−9)6)

3. Substitute these terms back into the original expression.

(log_)(x2)−(log_)((x−9)6)

4. Apply the Quotient Property, which states (log_)(a)−(log_)(b)=(log_)(a/b) to combine the two logarithms into a single term.

(log_)((x2)/((x−9)6))

Final Answer

2*(log_)(x)−6*(log_)(x−9)=(log_)((x2)/((x−9)6))

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