I need to find a function $f(x)$ such that the following data points would fit on it: $f(1) = 0 \\ f(2) = 0.5 \\ f(4) = 1.0 \\ f(8) = 1.5 \\ \cdots $ and so on. So the pattern is every time $x$ doubles $f(x)$ increases by $0.5$.
What is the equation for $f(x)$?