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

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- Feb 25th 2010, 07:01 PMmathhtamPLS HELP...Exponents and Logs
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 - Feb 26th 2010, 03:40 AMCaptainBlack
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