Richter Scale equation: $\displaystyle logE= 4.4 + 1.5M$
Suppose that the magnitudes of two earthquakes differ by 1 on the Richter Scale. Find the ratio of the released energy of the larger earthquake to that of the smaller earthquake.
Richter Scale equation: $\displaystyle logE= 4.4 + 1.5M$
Suppose that the magnitudes of two earthquakes differ by 1 on the Richter Scale. Find the ratio of the released energy of the larger earthquake to that of the smaller earthquake.
if I understand the question
first magnitude energy let it be
$\displaystyle \log E_1 = 4.4 1.5M $
natural log have the base 10 $\displaystyle \log_{10} E_1 = 4.4 + 1.5M $
so $\displaystyle E_1 = 10^{4.4 + 1.5M} $
second magnitude
$\displaystyle \log_{10} E_2 = 4.4 + 1.5(M+1) $
$\displaystyle E_2 = 10^{4.4 + 1.5(M+1)}$
$\displaystyle \frac{E_2}{E_1} = \frac{10^{4.4 + 1.5M + 1.5}}{10^{4.4+1.5M}}$
$\displaystyle \frac{E_2}{E_1} = \frac{10^{4.4}\cdot 10^{1.5M}\cdot 10^{1.5}}{10^{4.4}\cdot 10^{1.5M}} = 10^{1.5} $