# Thread: How to rearrange to find a variable value

1. ## How to rearrange to find a variable value

I have the following:

log (Ra / Rb) = -0.02 * C * T

I would like to find Ra = ?

Kindly help!

Thanks.

2. ## Re: How to rearrange to find a variable value

Originally Posted by Gunner123
I have the following:

log (Ra / Rb) = -0.02 * C * T

I would like to find Ra = ?

Kindly help!

Thanks.
Start by exponentiating both sides, making the base whatever the base of the logarithm is...

3. ## Re: How to rearrange to find a variable value

There is no base written to log so I assume it is 10.

would it be :

10 ^ (Ra / Rb) = 10 ^ (-0.02 * C * T)

I read an example on wikipedia
10 ^ 3 = 1000
log (1000) = 3

cheers!

4. ## Re: How to rearrange to find a variable value

Originally Posted by Gunner123
There is no base written to log so I assume it is 10.

would it be :

10 ^ (Ra / Rb) = 10 ^ (-0.02 * C * T)

I read an example on wikipedia
10 ^ 3 = 1000
log (1000) = 3

cheers!
No.

\displaystyle \begin{align*} \log{\left(\frac{R_a}{R_b}\right)} &= -0.02 \cdot C \cdot T \\ 10^{\log{\left(\frac{R_a}{R_b}\right)}} &= 10^{-0.02 \cdot C \cdot T} \\ \frac{R_a}{R_b} &= 10^{-0.02 \cdot C \cdot T} \end{align*}

Go from here.

5. ## Re: How to rearrange to find a variable value

ok thanks...I'm going for lunch now will be back

cheers!

6. ## Re: How to rearrange to find a variable value

Thanks, I also found the alternate working on the basis of:

Log (a/b) = log a - logb