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 times 2 times 3 or 2 squared times 3

3. Apply the product rule for logarithms, log a b equals log a plus log b to separate the factors.

4. Apply the power rule for logarithms, the log of a to the n-th power equals n log a to move the exponent of the factor 2 squared to the front.

Final Answer

log 12 equals 2 log 2 plus log 3

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