I think this is a really simple and stupid question, I am sorry for that, but I could not find anything while googling it.
why are covid-19 cases shown also on a logarithmic scale? on worldometer for example.
From my understanding, the ln(x) is the inverse function of the e(x) and so we could better see, if the curve flattens, when plotting the cases on a logarithmic scale? is this true?
On
The display on a logarithmic scale has mainly two reasons:
The range of the number of cases is very large. In the beginning there are only a few cases and at the highest point there may be several thousands of cases.
Using a logarithmic scale allows to present details at these different scales in a single graph. Otherwise we would just have a hockey-stick-graphs that all look much the same.
A related principle is to present graphs at a scale such that the prominent features have a slope of 45 degrees (see sparkline theory on Edward Tufte's blog).
The 45-degree principle relates to curves that grow exponentially fast and are in the beginning very flat and at the end very steep, that makes it very difficult to see differences between different curves.
The logarithmic scale will relate to the underlying mechanism. The growth rate of the cases is related to the logarithm
$$\underbrace{\frac{\frac{d}{dt}x}{x}}_{\text{growth rate}} = \underbrace{\frac{d}{dt} \log x}_{\text{change of logarithm}}$$
The slope of a curve on a logarithmic plot relates to the growth rate. See images like these:
Since COVID-19 is a viral disease, the number of people who get infected grows exponentially (until the curve hits the inflection point). Since exponential graphs grow really fast, its hard to study data from the graph normally.
When you graph them on a logarithmic scale, $\log a^x$ grows linearly since: $$\log a^x=cx$$ for $c=\log a$. This allows us to study the graph much easier (since it is a linear graph).