The Richter magnitude, R, of an earthquarge is given by,
R=0.67log(0.37E)+1.46
where E is the energy in kW X h released by the earthquake.
Show that E=2.7 X 10 ^(R-1.46)/0.67
You have:
$\displaystyle R=0.67 \log_{10}(0.37 E)+1.46$
so rearrange so that the $\displaystyle \log_{10}$ is on one side and everything else on the other:
$\displaystyle \log_{10} (0.37 E)=\frac{R-1.46}{0.67}$
By definition if $\displaystyle \log_{10}(a)=b$ then $\displaystyle a=10^b$, so:
$\displaystyle
0.37 E=10^{\frac{R-1.46}{0.67}}
$
and you should be able to finish it yourself from there.
CB