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I am not sure about how the log axis on a semilog plot works and I couldn't find information explaining that.

My questions:

  1. Just to make sure, are the values on the y-axis of a semilog plot calculated using y=10^x?
  2. Why are there different distances between the intervals on the y-axis? A visual on what I am referring to This is particularly confusing to me since the difference between 2 values should increase as the exponent becomes larger. However, the distances between the intervals on the graph decrease as the exponent increases.
  3. Why is there a repeated cycle of gradually-decreasing-in-the-length-of-the-intervals between y=10^x and y=10^(x+1)?
Claire
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1 Answers1

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This might help out your understanding a bit:

$$\log_{10}10=1, \log_{10}20=1.3, \log_{10}50=1.7$$

$$\log_{10}100=2, \log_{10}200=2.3, \log_{10}500=2.7$$ etc.

so you can see that the same factors (2x, 5x, etc.) always increase by the same linear amount (0.3, 0.7) from the current base factor of 10 (10, 100).

I hope this helps.

ad2004
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  • Hi, thanks for the reply, I didn't notice that! However, do you have any thoughts on why the distances between the intervals gradually decrease even if the numerical differences increase? Thanks again! – Claire Jun 05 '20 at 16:37