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What is Excel doing exactly when you tick the "logarithmic base 10" box under Format Axis?

It is taking log10, and then applying another transformation to get the transformed axis?

This is base on the posted question here:

Logarithmic scale in Excel chart with non-transformed axis labels

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For a log axis, Excel just calculates the logarithms of the data and plots that. Default is base 10, but can be chosen by the user (in Excel 2007 and later).

You can do the same thing manually by calculating a column of logs and using that as the data to plot. Then you have a linear plot of (say) log y vs x, and you can format the axes differently than you could with a logarithmic axis.

Two (almost identical) graphs are shown below. The first has a logarithmic y-axis, and the second uses calculated log (base 10) values for y. I don't know why grid lines are missing in the first graph. Gift from Excel, I guess.

But the point is that Excel just calculates the logs and plots them. And you can do the same thing if you wish.

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