Are logarithmic functions one to one?
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Answer:
As a function from (0,∞)→R, logarithms are one to one.
Explanation:
Considering the natural logarithm, it is the inverse of the exponential function ex:R→(0,∞), which is strictly monotonically increasing, so ln:(0,∞)→R is itself strictly monotonically increasing and one to one.
Any other logarithm is expressible as a constant multiple of ln, so is also one to one.
As a function from (0,∞)→R, logarithms are one to one.
Explanation:
Considering the natural logarithm, it is the inverse of the exponential function ex:R→(0,∞), which is strictly monotonically increasing, so ln:(0,∞)→R is itself strictly monotonically increasing and one to one.
Any other logarithm is expressible as a constant multiple of ln, so is also one to one.
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