How does the log axis on a semilog plot work?

Question

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? 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)?

Answer 1

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.