I multiply 100 by 1.05. I get 105. I multiply 105 by 1.05. I get 110.25. I multiply 110.25 by 1.05. I get 115,7625 and so on.
If I choose a fully random non-natural positive rational number, for example 240.353 What's the formula to determine how much I need to multiply 100 by 1.05 to get this number?
The only thing I know is that the number of times I have to multiply 1.05 to get any random non-natural number is also going to be non-natural.
Given an arbitrary positive rational number $y$, you are looking for a real number $x$ such that $$100 (1.05)^x =y $$ $$ 1.05 ^x = y/(100) $$
$$x= Ln ( y/100) /Ln (1.05)$$