This is very much dependent on your context and the purpose for which you might want to apply the logarithmic transformation. You did not provide enough detail to go really in depth with my answer. There are in general two main reasons to do something like this:
(1) In your model you believe that the transformation helps you to achieve better fit. For example you have a linear regression but think that the log transformed unemployment rate might be more linearly related to your dependent variable. This answer provides good treatment on this
(2) Also mentioned in the answer linked above. You want to control the way you interpret your model. Assuming a linear regression again, lets say that you have a model like this:
$$
P_{beer} = \beta_0 + \beta_1 unemployment\text{ }rate(\%) + u
$$
Where $P_{beer}$ is the price of beer across countries in USD. The interpretation would be, for 1% rise in unemployment rate (e.g. from 5 to 6%) there is $\beta_1$ USD change in $P_{beer}$. Alternatively, for:
$$
P_{beer} = \beta_0 + \beta_1 log(unemployment\text{ }rate(\%)) + u
$$
You would say that for 50% relative increase in unemployment rate (e.g. from 10% to 15%), $P_{beer}$ changes by $ 50* \frac{\beta_1}{100} $
There's plenty of resources on how to interpret linear regression, like here.
Back to your initial question: there is nothing in econometrics which could dictate you to use a logarithmic transformation on a variable of unemployment rate. Use it if it seems reasonable in your setting.
