Question

Are logarithmic functions one to one?

Answer 1

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.