On Richter scale, magnitudeMof an earthquake of intesityIis:

M= (ln(I)) - ln(I)_{0})/(ln(10))

Where I_{0}is the min intensity used for comparison, and assume that it equals 1.

a. Find intensity of 106 San Fran earthquake (M = 8.3)

This is what I did:

I plugged in the givens.

8.3 = (ln I - ln(1))/ln(10)

I know that ln(1) = 0 so that gets taken out

I get left with:

8.3 = (ln I)/(ln 10)

Not sure if I did this correctly... But I multiplied both sides by ln 10.

But then I got lost when there was another ln on the other side.

I think I forgot something that was crucial in order to find the variable of something with a natural log.

Can someone remind me or help me out?

Thanks

Answer: 10^{8.3}=199,526,231.5

I think this is what they did:

I converted the last thing I did into exponential (the part where I multiplied both sides by 10)

I=e^{ln10*8.3}... Oh wait I just figured it out, it equals the answer, but it doesn't look like the 10^{8.3}thing xD. But yeah, if anyone wants to explain to me how

e^{ln10*8.3}= 10^{8.3}that would be nice

Also

b. Find factor by which intensity is increased if Richter scale measurement is doubled

I'm not really sure what to first do.

The answer is: 10^{R}

So I'm assuming it was the base to the power of R?

Is it really just like that, or was there more steps before it?

Thanks