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If there is a exponential relationship $y = e^x$ and we take the logarithm of this we can see a linear relationship $\ln (y) = x$. So we could plot the logarithm of the y-axis values against the x values. Why does matlab do loglog plots, where the x-axis is also presented in logarithms? I see many plots where this is done.

Wouldn't using semilogy suffice? Or does using loglog or semilogy actually make no difference for a particular reason?

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    $y=c x^a \Leftrightarrow \log y = a \log x + \log c$ .2011-11-01
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    What @Raskolnikov's comment hints at is that loglog plots are designed to detect (approximate) **power laws** such as $y=cx^a$. To detect **exponential laws**, one would use semilog plots, as you suggest.2011-11-01

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