Use the definition of logarithms to translate among logarithms in any base.
Determine the conditions that make a logarithm defined
Problem
What conditions on \(b\) make \(\log_b(12)\) valid?
Big Picture
What this problem is really about
Check the argument and base independently. A real logarithm needs a positive argument, while its base must support a positive, one-to-one exponential inverse: it must be positive but cannot be one. Bases between zero and one are valid; they simply produce decreasing exponential functions.
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