Let be positive reals greater than 1, and
The only real solution of the equation can be uniquely written in the form for some integers and . Find .
Given that , and , let be the number of digits in . If is the first digit of , what is ?
Let be the number of times that the first digit of is with being an integer such that . What are the last three digits of
You may use the fact that
Details and assumptions
Greatest Integer Function / Floor Function: The function refers to the greatest integer smaller than or equal to . For example, and .