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