I think the explanation over complicates it.
On a natural log scale a 0.01 change in a coefficient (X) is approximately a 1% in response (Y). Where as a 0.01 change on a log10 scale is a 2.3% change in response.
Therefore Using the example if you see a 0.06 difference in coefficients on a natural log scale you know that the difference response is approximately 6%, whereas you'll need a calculator if it's on a log10 scale.
