# Transposition - HELP!!

• May 7th 2009, 10:34 AM
conners84
Transposition - HELP!!
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?

• May 7th 2009, 10:36 AM
e^(i*pi)
Quote:

Originally Posted by conners84
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?

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:

$\displaystyle y = \frac{e^{x-3}}{1+e^{x-3}}$
• May 7th 2009, 11:03 AM
conners84
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.