Given that x is a nonzero real number.
Determine the possible value(s) of x satisfying this equation:
(1+1/x)x+1 = (1+1/7)7
*** Adapted from a problem appearing in an Australian Mathematics Competition.
Lets start with some basic manipulation
(1+1/x)^(x+1)
= ((x+1)/x)^(x+1)
= (x/(x+1))^(-(x+1))
= (1-1/(x+1))^(-(x+1))
= (1+1/(-x-1))^(-x-1)
So then at this point its obvious that -x-1=7 -> x=-8 is a solution.
A quick sketch of the graph shows it is decreasing over its entire domain and has a shared horizontal asymptote of y=e, so x=-8 is the only real solution.
Solution
