How do I rearrange this equation to solve for B?

[martine]

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...

Help, please?

 

[HallsofIvy]

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]

Suppose you have the equation:

A=C*B^d.

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

 

[rhit2013]

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

 

[CellCoree]

It's completely normal to get stuck on equations, even as a scientist. Don't be ashamed to ask for help! It's important to always double check your calculations and make sure you're using the correct units and values.

To rearrange this equation to solve for B, we need to isolate B on one side of the equation. We can do this by dividing both sides of the equation by 1.27 and then raising both sides to the power of 1/0.45.

So the equation would become:

B = (A/1.27)^(1/0.45)

To solve for B, simply plug in the given value of A (2.5) and solve using a calculator or by hand. This should give you the value of B.

It's important to note that in empirical relationships, there may be some discrepancies between calculated and actual values due to experimental error or other factors. It's always a good idea to check your calculations and make sure they make sense in the context of the problem.

I hope this helps! Don't hesitate to reach out if you need further assistance.