just for curiosity,is this problem has anything to do with chemistry ?
Howdy folks. First time poster here
Have a bit of a problem and can't seem to figure the correct way to solve it
I'm looking for Ka
0.93Ka - 1.969 = -e^(-2Ka)
Any ideas in how to solve it? I was planning on taking LN of both sides, but that still leaves me with LN of Ka on one side with Ka on the other side of the equation, which is practically the same.
Hello FreemasonFurbie
Welcome to Math Help Forum!You won't be able to find an algebraic solution. Your best bet is a numerical method. With a spreadsheet, I've just found a couple of solutions: one negative and one positive. To 4 d.p. they are:
I hope that helps.
Grandad
Hello FreemasonFurbieNothing very subtle - trial and error, really. I just set up the function 0.93x+exp(-2x) and tried some likely values around x=0. Then refined them when I got a general feel for the behaviour of the function.
Without a spreadsheet I should use Newton's Method - but to be honest it's loads quicker just to stick some numbers into Excel! (You'd never think I was a real mathematician, would you?)
Spreadsheet attached (for what it's worth!)
Grandad