Question 926246
<pre>
e<sup>14x</sup>+5e<sup>7x</sup>-14 = 0

Let   e<sup>7x</sup> = u
Then  (e<sup>7x</sup>)<sup>2</sup> = u<sup>2</sup>
or    e<sup>14x</sup> = u<sup>2</sup>

u<sup>2</sup>+5u-14 = 0

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

u-2 = 0;    u+7 = 0
  u = 2      u = -7
            
 e<sup>7x</sup> = 2     e<sup>7x</sup> = -7  <-- no real solut to this since left side is positive
this is 
equivalent 
to equation

7x = ln(2)
 x = {{{ln(2)/7}}}   <--- only solution                 
            
Edwin</pre>