Hello

I am new to this forum so therefore please accept my apologies if I have not posted this problem to the correct forum.

x=5+ln(y/(y-1))

I am trying to break out of the brackets to the above problem

Please can someone confirm that I have gone about it correctly.

Also can you confirm that I have solved forYcorrectly. I am not confident with this at all.

1) we know that natural logln(a/b) = ln a - ln btherefore

2)ln(y/(1-y)) = ln y - ln(1-y)therefore

= ln y - ln( -y + 1)

= ln y - ln (1/y) + ln 1

x = ln y - ln 1 - ln y + ln 1 + 5

3) Ok now to getYon its own.

ln y - ln 1 - ln y + ln 1 + 5 = xso

ln y - ln 1 + ln 1 - ln y + ln 1 + 5 = x + ln 1

ln y - ln y + ln 1 + 5 = x + ln 1

ln y - ln y + ln y + ln 1 + 5 = x + ln 1 + ln y

ln y + ln 1 + 5 = x + ln 1 + ln y

ln y + ln 1 - ln 1 + 5 = x + ln 1 + ln y - ln 1

ln y + 5 - 5 = x + ln 1 + ln y - ln 1 - 5

ln y = x + ln 1 + ln y - ln 1 - 5

ln y / ln y = x + ln 1 + ln y - ln 1 - 5 / ln y

1ory = x + ln 1 + ln y - ln 1 - 5 / ln yThanks for your time

This is how I am seeing it at the moment, I know that this cannot be right as the quotient equation for Y would be undefined as the denominator is equal to zero!