How would I transpose this equation to solve for A when B is known?

Question

B = 0.0093A^2.6645

Answer 1

B = 0.0093A^2.6645 take each side to the 1/2.6645
B^1/2.6645=.0093^1/2.6645*A divide bt .0093^1/2.6645
A=(B/.0093)1/2.6645
A=5.787B^.3753

Answer 2

The first step is to get rid of 0.0093 on the A side of the equation by dividing both sides by 0.0099. You get
107.5269B = A^2.6645 (1)

The next step is to get rid of the exponent. This can be done using logarithms. But there is an easier way if you don't know logs or don't have access to the logarithm tables or a scientific calculator.
We know that when an expression is raised to a power, all we need to do is multiply the exponents to minimize it. in this case, we want A to be raised to a power of 1. So, what do we need to multiply the exponent 2.6645 by in order to get 1: i.e 2.6645x = 1.
So, x is 1/2.6645 = 0.3753.

Therefore, raining both sides to the power of 0.3753 will give you A by itself: So, using equation (1) above:
(107.5269B)^0.3753 = (A^2.6645)^0.3753
(107.5269B)^0.3753 = A

Ultimately though, you will need logarithmic table to resolve this equation..

Answer 3

B/0.0093 = A^2.6645
log B/0.0093 = log A^2.6645
log B - log 0.0093 = 2.6645 log A
1/2.6645(log B - log 0.0093) = log A
A = 10^(1/2.6645(log B - log 0.0093))

yupchagee's way works too, and avoids logs.

Answer 4

I would take the natural log of both sides. I think that saves a little work. Then you would get:

ln B = ln (0.0093) + (2.6645) ln A
ln B - ln (0.0093) = (2.6645) ln A
{[ln B - ln (0.0093)]/2.6645} = ln A
A = e^{[ln B - ln (0.0093)]/2.6645}