What is the magnitude of an earthquake that is 10,000 times more intense than a standard earthquake

In the equation you showed, I is the intensity of the earthquake and S is the intensity of a standard earthquake. The magnitude of this last one is “log S/S=0”. So, in the Richter Scale 0 is the same of the log of an earthquake with magnitude of 10. If we elevate 10 4 times, we reach to 10000, the times in the problem above. So, Richter Scale of '4' = lof(10⁴) = log(10000) = earthquake with a magnitude of 10000.

With this explained, you can notice how 4 is the correct answer.  

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: