Logs & Exponents

[mathmaks]

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

 

[mmm4444bot]

They are asking you to solve the given equation for E.

Since E appears as part of the input to the logarithmic function, we'll need to eventually switch to exponential notation (in order to get E outside of the parentheses).

But, before we switch to exponential notation, we first need to isolate the logarithm to one side.

In other words, begin by performing the usual algebraic manipulations to both sides of the given equation, to arrive at the following form.

log(0.37 E) = everything else on the RHS (righthand side)

Can you do that?

Cheers ~ Mark