"But that really gives a different magnitude to ..."

Using log base 10 \(because those are easier to do in your head\):

But that really gives a different magnitude to the evidence. Why not be consistent with the log base?

For example, if we were to use log base 2, the prior would be ~16.6 magnitudes strong and the evidence ~8. This means that the evidence would alter the prior by (slightly) less than half the order of magnitudes, where's in the case of log base 10 the alteration is (slightly) more than half the order of magnitudes (5 vs 2.7).

Also, imagine the absurd choice of log base 100k. The prior would remain practically intact in terms of this kind of order of magnitudes.