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What is the domain of the logarithmic function y = log base a of x?
AEvery positive number
BEvery real number
CEvery whole number
DEvery negative number
Answer & Solution
Correct answer: A. Every positive number
1. A logarithm asks what exponent the base needs in order to reach the input.
2. An allowed base raised to any power comes out positive, so only positive inputs can be reached.
3. The domain is therefore every positive number, and the graph never touches the vertical axis.
4. The range, by contrast, is every real number, since the exponent can be anything.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_