A few days ago, my Calculus professor discussed exponential functions in general. Apart from the easy stuff, he actually asked us something that caught my attention and yet puzzled me greatly. The problem at hand was the following:
Approximate , where ?
Furthermore, he mentioned that this can be solved using techniques for different representation of real numbers. This is something I have never come across thus far, and would love it if someone gave me a more thorough explanation if possible.
Needless to say, I would also like to see this problem generalized a bit.
Therefore, my questions are:
Given that , where and are real numbers, is there a valid way of finding ? If so, how does one do it and can you provide a valid proof?
Thank you very much in advance!
Note: Feel free to point at any literature that can answer my questions.