find the inverse of the following function?

Question

q(x)= ln(x+3) - ln(x-5)

Answer 1

q(x) = ln[(x + 3)/(x - 5)]

Switch q and x, and find q again in terms of x.

x = ln[(q + 3)/(q - 5)]

e^x = (q + 3)/(q - 5)

qe^x - 5e^x = q + 3

q(x) = (3 + 5e^x)/(e^x - 1)

Answer 2

y= ln[(x+3)/(x-5)]

so e^y = (x+3)/(x-5) so x e^y -5 e^y = x+3
x(e^y-1)= 5e^y+3
x= (5e^y+3)/(e^y-1)

interchange x and y
y=(5e^x+3)/(e^x-1)