HELP!!
Can anyone help me transpose the following forumla. It's driving me crazy!
x = 3 + ln(y/(1 - y))
I need to make y the subject, any ideas?
Thanks in advance
Take 3 from both sides:
$\displaystyle x-3 = ln(\frac{y}{1-y})$
Raise e to both sides:
$\displaystyle e^{x-3} = \frac{y}{1-y}$
$\displaystyle (1-y)(e^{x-3}) = y$
Distribute the 1-y:
$\displaystyle e^{x-3} - ye^{x-3} = y$
Add $\displaystyle ye^{x-3}$ to both sides:
$\displaystyle e^{x-3} = y+ye^{x-3}$
Factor the RHS:
$\displaystyle y(1+e^{x-3}) = e^{x-3}$
Dividing:
$\displaystyle y = \frac{e^{x-3}}{1+e^{x-3}}$
will this still work if i have values for x of 1,3 and 10. i have tried plugging these values in but im not getting the answer i would have expected. the value for x are supposed to be years and the value of y a probability of breakdown but y for 10 years is -1.