Given a value in log scale, get the equivalent value in a linear scale

Question

I have a graph with an $x$-axis in a log scale. I have the same graph in a linear scale. Given a value in the log scale, I want to find that value in the linear-scale graph.

It is further complicated a bit by the fact that the log graph starts at $10$, whereas the linear graph starts from $0$.

Answer 1

One simple function $f\colon [10, 10000] \to [0, 1325]$ is given by: $$ f(x) = \frac{1325}{3} \left( (\log_{10}x) - 1 \right) $$