SOLUTION: Solve e^(14x)+5e^(7x)-14=0 giving solution(s) in natural logarithm form.

e14x+5e7x-14 = 0

Let   e7x = u
Then  (e7x)2 = u2
or    e14x = u2

u2+5u-14 = 0

(u-2)(u+7) = 0

u-2 = 0;    u+7 = 0
  u = 2      u = -7
            
 e7x = 2     e7x = -7  <-- no real solut to this since left side is positive
this is 
equivalent 
to equation

7x = ln(2)
 x =    <--- only solution                 
            
Edwin