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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.

pic of graph

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

lioness99a
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StupidQuestions
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1 Answers1

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

Adriano
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  • Thank you! If you don't mind me asking, where does the 3 come from? – StupidQuestions Jul 18 '17 at 08:30
  • After logging $10, 100, 1000, 10000$, we get $1, 2, 3, 4$. We linearly interpolate the points $(1, 0)$ with $(4, 1325)$. The slope of this line is $\frac{1325 - 0}{4 - 1}$. – Adriano Jul 18 '17 at 09:58