Question

An earthquake near New Zealand measured 4.2
on the Richter scale. Use the formula r=log(a/a0)
to determine approximately how many times stronger the wave amplitude of the earthquake was than A0
.

Answer 1

Richter magnitude uses base-10 logs: r = log10(a/a0). So
a/a0 = 10^r = 10^4.2 = 10^(4+0.2) = 10^4·10^0.2 ≈ 10000·1.5849 ≈ 1.5849×10^4.

The earthquake’s wave amplitude was about 1.58×10^4, or roughly 15,800 times, that of A0.