Relate a function's domain to its equation, graph, and context, especially when model choice matters.
Find the domain of a logarithmic function by requiring its argument to be positive
Problem
What is the domain of \(f(x)=\ln(x-6)\)?
Big Picture
What this problem is really about
Logarithmic domains use a stricter boundary rule than square roots. Require the entire argument to be positive, solve that inequality, and test the boundary by imagining the argument becoming zero. Since a real logarithm is not defined there, the domain starts with an open endpoint rather than an included one.
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