Use logarithm properties to simplify numeric logarithmic expressions and estimate values.
Simplify logarithmic expressions using the power law
Problem
What is a simplified form of \(3\log_2(4)\) using the power law of logarithms?
Big Picture
What this problem is really about
The power law moves a multiplier outside a logarithm onto the argument as an exponent; it does not multiply the argument or alter the base. Once the powered argument is rewritten as a power of the logarithm’s base, the logarithm simply reports that exponent. Evaluating before applying the multiplier checks the same structure in reverse.
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