Simplify/Condense 3 log of x+4 log of x-2

Problem

3*(log_)(x)+4*(log_)(x−2)

Solution

1. Apply the power property of logarithms, which states n*(log_)(a)=(log_)(an) to both terms in the expression.

(log_)(x3)+(log_)((x−2)4)

2. Apply the product property of logarithms, which states (log_)(a)+(log_)(b)=(log_)(a*b) to combine the two logarithmic terms into a single logarithm.

(log_)(x3*(x−2)4)

Final Answer

3*(log_)(x)+4*(log_)(x−2)=(log_)(x3*(x−2)4)

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