# Alaska experienced an earthquake of magnitude 8.7 on the Richter scale in February 1965. The earthquake in Indonesia in 2004 was 4 times as strong as the Alaskan one. So what was its approximate magnitude on the Richter scale?

$\approx 9.1$
Assuming that $4$ times as strong means releasing about $4$ times the energy, note that the energy release is the $\frac{3}{2}$ power of the amplitude and the magnitude (as measured on the Richter scale) is based on the common (base $10$) logarithm of the amplitude.
$8.7 + \log \left({4}^{\frac{2}{3}}\right) = 8.7 + \frac{2}{3} \log \left(4\right) = 8.7 + \frac{4}{3} \log \left(2\right) \approx 8.7 + \frac{4}{3} \cdot 0.3 = 9.1$