Question 998138
{{{ln(y)-ln(y+1)=ln(x)}}} Start with the given equation



{{{ln(y/(y+1))=ln(x)}}} Use <a href="http://www.purplemath.com/modules/logrules.htm">rule 2</a>



{{{y/(y+1)=x}}} See note below



{{{y=x(y+1)}}} Multiply both sides by y+1.



{{{y=xy+x}}} Distribute



{{{y-xy=x}}} Subtract xy from both sides.



{{{y(1-x)=x}}} Factor



{{{y=x/(1-x)}}} Divide both sides by 1-x.



Note: if {{{log((x))=log((y))}}}, then {{{x=y}}}. This is true for any log of any base.