Are logarithmic functions one to one?

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Are logarithmic functions one to one?

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Answer 1 · 2015-10-24T22:52:43

As a function from #(0, oo) -> RR#, logarithms are one to one.

Explanation:

Considering the natural logarithm, it is the inverse of the exponential function #e^x:RR -> (0, oo)#, which is strictly monotonically increasing, so #ln:(0, oo) -> RR# 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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Are logarithmic functions one to one?

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