Question

I'll give a medal and become a fan of anyone who can help me solve this:

"The Richter scale is used to measure the magnitude of an earthquake. The magnitude, R, is given by the equation R = 0.65log(0.39E) + 1.45, where E is the energy (measured in kilowatt-hours) released by the earthquake. Determine the amount of energy released by an earthquake of magnitude 7.5"

Answer 1

I already plugged in 7.5, so 7.5 = 0.65log(0.39E) + 1.45

Answer 2

I just don't know how to solve for E from there.

Answer 3

Oh, I guess I could move the 1.45.

6.05 = 0.65log(0.39E)

Answer 4

@phi ? Again I'm sorry to keep tagging you ._. I try to wait until someone else comes to help but usually nobody does.

Answer 5

there is one other "obvious" step. how do you get the log() by itself on the right side ?

Answer 6

hmm.. divide both sides by 0.39E?

Answer 7

oh wait...

Answer 8

divide by 0.65?

Answer 9

I'm not quite sure...

Answer 10

the way to remember (or figure it out) is
if you have

2x = 5
if you divide 2 by itself you get 1
so divide both sides by 2
x = 5/2

in this case
0.65log(0.39E) = 6.05
and you want to make the "0.65 go away"

Answer 11

0.65 divided by itself is 1

Answer 12

oh okay so then it would end up being log(0.39E) = 6.05/0.65 or log(0.39E) = 9.308 (rounded)

Answer 13

right?

Answer 14

yes, that is good.

next, we get rid of the log. make the log the exponent of the base
this is hard to say but we do it this way:

log(a) (base 10)
is "undone" by 10^log(a)
which gives a

Answer 15

if we start with
log(0.39E) = 9.308

make each side the exponent of the base of the log (10 is assumed)
10^(log(0.39E) ) = 10^9.308

that ugly stuff on the left side is 0.39E (we undid the log)

0.39 E = 10^9.308

Answer 16

solve for E by dividing by 0.39

Answer 17

oh okay (: hold on I'll post my answer once I have it

Answer 18

For my final answer I got E = 5,211,171,822.913

Answer 19

I would round that to E = 5.21 * 10^9 kw-hours
in scientific notation.