Solve for x, (1+a/x)^x = b here a & b are constants

Question

Solve for x, (1+a/x)^x = b here a & b are constants

Answer 1

let a = b = 1

(1+1/x)^x = 1

xln(1+1/x) = ln1= -

x = 0 or ln(1+1/x) = 0

1+1/x = 1, 1/x = 0, x = infinity'

x=0 won't work as that makes denominator 0 inside the parentheses

no real solution if a = b

a can't = b

b = 2.5a works though, then x = 2

(1+1/x)^x = 100

let x = 2

(1+1/2)^2 = (3/2)^2 =9/4 = 2.5