This is my first time posting here, or in any math forum, and I really need help.
I was working on an assignment on compounded interest and out of nowhere I see this problem about the Richter scale, which I have no idea how to solve. enter image description here
My best guesss has been to try to replace the R by the values mentioned in the problem and then change the log to exponential form, but I still don't have the answer and I am pretty sure that what I got is completely wrong.
This is my development of the problem, just in case.
$3=log(\dfrac{I}{I0}) \Rightarrow 10^3= \dfrac{I}{I0} \Rightarrow 1000\times I0=I $
$8.25=log(\dfrac{I}{I0}) \Rightarrow 10^8.25=\dfrac{I}{I0} \Rightarrow 10^8.25\times I0=I$
$(10^{8.25} \times I0=I)$ / $(10^{8.25} \times I0=I) $
Please, Could you help me with this? I would very much appreciate it.
From the definition,
$(10^R)$ is linearly proportional to $I$.
That is, $~\displaystyle (10^R) = I \times \frac{1}{I_0}.$
Therefore, the ratio of the intensities is
$$\frac{(10)^{(8.25)}}{(10)^{(3)}} = (10)^{(5.25)}.$$