Thread: Rearranging formulae

1. Rearranging formulae

I need to know how to do the following examples of theory questions relating to rearranging formula:
1. a/p ln (b-2T) = P, find T
2. T= RC/t log (Vt/Vo) ,change to Vt
3. 5(^3x+2) = 3(^2-x), change to x
Any help would be great, thanks

2. 1. $\displaystyle \frac{a}{p} ln (b-2T) = P$
$\displaystyle ln (b-2T)=\frac{Pp}{a}$
$\displaystyle (b-2T)=e^\frac{Pp}{a}$
$\displaystyle 2T=b-e^\frac{Pp}{a}$
$\displaystyle T=\frac{b-e^\frac{Pp}{a}}{2}$

2. $\displaystyle T= \frac{RC}{t} log \frac{Vt}{Vo}$
$\displaystyle log \frac{Vt}{Vo}=\frac{Tt}{RC}$
$\displaystyle \frac{Vt}{Vo}=e^\frac{Tt}{RC}$
$\displaystyle Vt=Voe^\frac{Tt}{RC}$

3. thanks for that Alex, I had the right method just was getting confused. I dont even know where to start with the third one.

4. $\displaystyle 5^{3x+2} = 3^{2-x}$

$\displaystyle 3^{\frac{log 3}{log 5}(3x+2)}=3^{2-x}$

Then, $\displaystyle {\frac{log 3}{log 5}(3x+2)}={2-x}$

Er, plausible? not really sure, just a suggestion

5. For that last one, this is what I came up with...

5(^3x+2) = 3(^2-x), change to x

ln5 (^3x+2) = ln 3(^2-x)
(3x+12) ln5 = (2-x) ln3 3xln5= (-2) -(2-x) ln3
3x+2 = (2-x)ln3/ ln5 3x ln5 = -x ln3

3x = -x ln3/ln5

Don't know if that is correct.I am also finding these difficult...

ln (y + 5) = 3.1, solve for Y

4 (^x+1) = 6^0.5x, solve for x

I= Imax (1 -e^ -30t/0.01), find T

again, any help would be appreciated