Question

The magnitude of an earthquake is found by the equation M=2/3 log E/10^118, where M is the magnitude and E is the energy released. Find the magnitude of an earthquake that released 10^203 ergs of energy.

Answer 1

\[M = \frac{2}{3} \log{\frac{10^{203}}{10^{118}}} \]

Is this correct?

Answer 2

And that is a base 10 log, right, not a natural log?

Answer 3

yeah, I just need help solving it

Answer 4

Okay, can you simplify\(\frac{10^{203}}{10^{118}}\)?

Answer 5

no?...

Answer 6

How about \(\frac{10^3}{10^1}\), what does that equal?

Answer 7

100

Answer 8

Right, 100 is \(10^2\) or \(10^{3-1}\) so subtract the powers.

Answer 9

ok so it'd be 10^85

Answer 10

Cool. So what is \(\log_{10}{10^{85}}\)?

Answer 11

85

Answer 12

You good from here?

Answer 13

yes tysm

Answer 14

Cheers