Question

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

Answer 1

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

Explanation:

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

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

Explanation:

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))`