Question

Are logarithmic functions one to one?

Answer 1

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.