# Thread: PLS HELP...Exponents and Logs

1. ## PLS 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

2. Originally Posted by mathhtam
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