[Math] How to get equation for semilog graph

graphing-functions

I would like to get equation for a known graph "speech banana" enter image description here

So, It happens to have be something like two joined $x^2$ equations. One starts on
$ (1000,65) $ and other $ (1000,40)$.

So If I would be on linear graph I could just join both $x^2$ something like $ 0.5x^2 $ and $0.45x^2 – 20$ but as I am on semilog graph I do not know what approach to use.

What would be the best approach to get the equation of this kind of graph?

Best Answer

You could use the logarithm of $x$ as the input to your quadratic.

So (with base $10$ logarithms) the bottom curve would be something like:

$y = 65+40*(\log_{10}(x)-3)^2 $

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