Question 1042521
<pre><b>

I use "ln" instead of "log<sub>e</sub>.

You took natural logs of both sides too soon.
Wait until you've solved for e<sup>x</sup>.

{{{y}}}{{{""=""}}}{{{(e^x)/(1-e^x)}}}

 First multiply both sides by 1-e<sup>x</sup>

{{{y(1-e^x)}}}{{{""=""}}}{{{e^x}}}

Distribute

{{{y-ye^x}}}{{{""=""}}}{{{e^x}}}

Isolate the terms in e<sup>x</sup>:

{{{y}}}{{{""=""}}}{{{ye^x+e^x}}}

Factor out e<sup>x</sup> on the right:

{{{y}}}{{{""=""}}}{{{e^x*(y+1)}}}

Divide both sides by y+1

{{{y/(y+1)}}}{{{""=""}}}{{{e^x}}}

Take natural logs of both sides:

{{{ln(y/(y+1))}}}{{{""=""}}}{{{x}}}

{{{x}}}{{{""=""}}}{{{ln(y/(y+1))}}}

Edwin</pre></b>