Solve for y if ln(y-1)=X+lny?

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Answer 1 · 2018-05-28T11:11:45

#y=1/(1-e^x)#

We have
#ln(y-1)-ln(y)=x#
so
#ln((y-1)/y)=x#
#(y-1)/y=e^x#
#11/y=e^x#
#1-e^x=1/y#
so
#y=1/(1-e^x)#

Answer 2 · 2018-05-28T11:16:43

#y=(1/(1-e^x))#

Using Property of logarithm

#ln(a/b)=ln(a)-ln(b) #
#ln(y-1)-ln(y)=x#

#ln((y-1)/y)=x#

Now take antilog
#((y-1)/y)=e^x#

Simplify above equation
#y=(1/(1-e^x))#