Question

Help
what is the inverse of:
y = (e^x)/(1+7e^x)

I got:
y = (e^x)/(1+7e^x)
x = (e^y) / (1 + 7e^y)
x + 7xe^y = e^y
x = e^y - 7xe^y
x = (e^y)(1 - 7x)
(x)/(1 - 7x) = e^y

How would I bring down the y?
Thank you.

Answer 1

take the natural log (ln) of both sides
\[\ln (x/(1-7x)) = \ln(e ^{y})\]

Due to the properties of logs, the y can be dropped, and ln(e) = 1

Therefore:
y = ln(x/(1-7x))

Answer 2

I see ok thanks.
ill try it out.

Answer 3

Thanks. it workwed