How can I isolate for the $z$ exponent?

Question

Can anyone help me with this math equation?

Solve for $z$

$$P = \frac{e^z}{1 + e^z}$$

$$P(1 + e^z) = e^z$$

$$P + Pe^z = e^z$$

$$P = e^z - Pe^z$$

I've got this far, am I at least on the right track? Not sure exactly what to do next.

Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? — Hippalectryon, Mar 05 '15 at 16:44

score 1 · Answer 1 · answered Mar 05 '15 at 16:46

1

Hint: $P= \frac{e^z+1-1}{e^z+1}=1-\frac{1}{e^z+1} $

answered Mar 05 '15 at 16:46

GFR

score 1 · Answer 2 · answered Mar 05 '15 at 17:42

1

You are on the right track. Now that you are at

$$P = e^z -Pe^z$$

Factor out $e^z$, that is

$$P = e^z(1-P),$$ and dividing yields

$$\frac{P}{1-P}=e^z.$$

We finish off by using the logarithm

$$z = \ln\left(\frac{P}{1-P}\right). $$

answered Mar 05 '15 at 17:42

Eff

2 Answers2