I think it will never again be so close.
If on the other hand you consider 2^x / 10^y or vice versa you can get this close to 1.
For example and this gives 59/196 as a good approximation of for whatever that's worth.
If we have 2^3, itīs distance from 10^1 is only 2.
If we have 2^10, itīs distance from 10^3 is 24 (as 2^10=1024 and 10^3=1000).
Is there any other natural number pair x,y which results distance between 2^x and 10^y to be only 2?
Is there any formula, where to insert desired distance and find x and y as a result, or does it only requires raw computer power to find an answer?
I think it will never again be so close.
If on the other hand you consider 2^x / 10^y or vice versa you can get this close to 1.
For example and this gives 59/196 as a good approximation of for whatever that's worth.
No, it won't be as close as 2.
For numbers , we have:
This can only be true if and are relatively prime (Euclid).
That means that y-1=0.
So the only solution for a distance of 2 is: and .