# Rearranging equations

I'm almost a bit ashamed to ask, but for some reason I'm stuck. Being a bit thick today I guess.

Given is an empirical relationship
A = 1.27*B^0.45
A = given. Say 2.5

What is B?

For some reason, if I take a random but plausible B and calculate A, I get a different result then when I take the resultant A and try to result at the B I just made up. Either I can't rearrange equations anymore, or this relationship only works in one direction. Sounds silly...

HallsofIvy
Homework Helper
It would have helped if you had shown exactly what numbers you used and what numbers you got.

If, for example, we take B= 5, then A= 1.27(5^.45)= 1.27(2.0632)= 2.6202. Going the other way, if A= 2.6202, then 2.6202= 1.27(B^.45) so B^.45= 2.6202/1.27= 2.0632 and then B= (2.0632)^(1/.45)= 2.0632^2.222= 4.999 which rounds to 5.

That rounding may be what you are talking about. Even if you use a calculator which shows, say 10 decimal places, it is working, internally, to several more decimal places so you can't expect to get exactly what you started with- it should be the same up to the last one or two decimal places, however.

arildno
Homework Helper
Gold Member
Dearly Missed
Suppose you have the equation:

A=C*B^d.

Then, B, in terms of the other numbers is:
B=(A/C)^(1/d)

Simple.
Take 2.5/1.27 and get 1.969
Take 1.969 and raise it to the (1/.45).
You get 4.507.