Equation involving floor function:

Question

Given n a natural number, find $x$ (positive real number) such that: $$ 6\lfloor x \rfloor=n, $$ where $ \lfloor x \rfloor $ represents the value of the floor function in x.

Answer 1

For $n>1$, a solution is $$x=(n+1)^{1/n}.$$ To prove it, use induction to show that $n+1<2^n$ for all $n>1$.