Expand the Logarithmic Expression log of 12

Problem

(log_)(12)

Solution

1. Identify the number inside the logarithm as a composite number that can be broken down into its prime factors.

2. Factor the number 12 into its prime components, which are 2×2×3 or 2×3

3. Apply the product rule for logarithms, (log_)(a*b)=(log_)(a)+(log_)(b) to separate the factors.

4. Apply the power rule for logarithms, (log_)(an)=n*(log_)(a) to move the exponent of the factor 2 to the front.

Final Answer

(log_)(12)=2*(log_)(2)+(log_)(3)

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