# Rearranging formula

• Oct 7th 2012, 10:58 PM
Rpenguin
Rearranging formula
Hello all, i need to rearrange this formula to make E the subject (E=)

M= 0.67 log (0.37 E) +1.46

While i can rearrange most formula, the ones that contain log seem to confuse me.

• Oct 8th 2012, 12:40 AM
chiro
Re: Rearranging formula
Hey Rpenguin.

To get rid of a log(x) term to get an x, you have the exponential of it. So as an example, if I have y = log(x) and I want to get x, then I take the exponential of both sides which gives exp(y) = exp(log(x)) = x which gives exp(y) = x.
• Oct 8th 2012, 01:22 AM
Rpenguin
Re: Rearranging formula
Thanks Chiro, I understand what you are saying but am unsure of how to then take this and then use it on my original formula.
• Oct 8th 2012, 01:27 AM
chiro
Re: Rearranging formula
Show us what you have got in terms of one side with a log term and the other side with the rest of the relationship.
• Oct 8th 2012, 01:51 AM
Rpenguin
Re: Rearranging formula
Here : M= 0.67 log (0.37 E) +1.46 The M value is for example 4.7 but it needs to be rearranged so that the E value can be found.

Thanks again
• Oct 8th 2012, 02:08 AM
chiro
Re: Rearranging formula
Can you please get an expression in terms of log(0.37 E) = something else? (I can provide hints, but I try not to do the whole thing for someone).
• Oct 8th 2012, 02:19 AM
Rpenguin
Re: Rearranging formula
As in log(0.37E) = M-146
......................... 0.67

If not, im sorry but I am not sure.
• Oct 8th 2012, 02:41 AM
chiro
Re: Rearranging formula
That's good. Now I take the exponential of both sides giving us:

0.37E = exp[(M-1.46)/0.67] and finally, E = (1/0.37)*exp[(M-1.46)/0.67]
• Oct 8th 2012, 03:02 AM
Rpenguin
Re: Rearranging formula
Thanks a heap, Chiro!
• Oct 8th 2012, 10:03 PM
Rpenguin
Re: Rearranging formula
Sorry to bother you again, Chiro, but if you were to enter this on a graphical calculator to find E how would you do this? Is there an "exp" button that i am missing? Just to compare answers, what value for E do you get if M = 9.5?
• Oct 8th 2012, 10:12 PM
chiro
Re: Rearranging formula
There are usually two types of logarithms: base 10 and base e. In terms of exponential, there is a button (usually its called e^x or exp(x)) and that will take the exponential in base e. If it's base ten then you simply calculate 10 to the power of the number to get the exponential in base 10.

Using a common computer package called R, I get the answer:

> (1/0.37)*exp((9.5-1.46)/0.67)
[1] E = 439877.81464595574653

If I use base 10 I get:

> (1/0.37)*10^((9.5-1.46)/0.67)
[1] 2702702702702.6914062

The reason I include base 10 is that unfortunately, sometimes people use log to mean log to the base 10 rather than to the natural base and it's a real pain in the neck when people say log(x) is log base 10 instead of log base e.

One thing though is that if you see ln(x) this is always base e no matter what.