Rearranging formulae

**Tino1210** · June 1st 2009, 04:38 AM

I need to know how to do the following examples of theory questions relating to rearranging formula:

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

Any help would be great, thanks

**alexmahone** · June 1st 2009, 04:47 AM

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

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

**Tino1210** · June 1st 2009, 05:32 AM

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

**Singaporean** · June 1st 2009, 06:39 AM

$5^{3x+2} = 3^{2-x}$

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

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

Er, plausible? not really sure, just a suggestion

**Tino1210** · June 8th 2009, 11:58 AM

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

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