I was a criminal intelligence analyst for a decade, then a consultant in that kind of thing. I've never seen crime data portrayed like this, for good reason.
Logarithmic scales are used to compress exponential differences (bacteria multiplying, stock markets doubling year on year, differences between towns and cities).
In the Economist's case, a log scale would make sense if there was a reason for Afghan men to commit more of these crimes (if each Afghan had a hundred cocks, or was actually ten men inside one suit). But there isn't. The log scale just obscures the vastly higher rates of offending by these imported Labour voters.
The casual reader will skim over it and assume it's a linear scale. The one advantage is that it makes proportional differences below/close to the baseline easier to see. But it obfuscates the truth.