you do not need to be a mathematician to understand that what you are looking is .........IMPOSSIBLE.
Hello,
I am far from being a mathematician and as such am struggling rearranging the following equation as such as would make W*L the subject:
I =2*n*F*C*D*L*[1/ln(4*D*t /W^2)]
I'd be very grateful for the rearrangement of this and more importantly an explanation as to the best method to do so!
Thank you very much in advance!
Well, you can't have "both" W and L as subjects but you can have either W or L.
To solve for L, from I =2*n*F*C*D*L*[1/ln(4*D*t /W^2)] multiply both sides by that denominator, ln(4Dt/W^2), to get
Iln(4Dt/W^2)= 2nFCDL
and then ust divide by 2nFCD to leave on "L" on the right:
2InFCDL ln(4Dt/W^2)= L
To solve for W, start, as before, by multiplying both sides by ln(4Dt/W^2):
Iln(4Dt/W^2)= 2nFCDL
Now use the properties of the logarithm on the left to get I(ln(4Dt)- 2ln(W))= Iln(4Dt)- 2Iln(W)= 2nFCDL
Subtract Iln(4Dt) from both sides: -2Iln(W)= 2nFCDL- Iln(4Dt)
Divide both sides by -2I: ln(W)= -nFCDL/I- ln(4Dt) and, finally, take the exponential of both sides
W= e^{-FCDL/I- ln(4Dt)}= (e^{-FCDL/I})/e^{ln(4Dt)}= e^{-FCDL/i}/4Dt.