Question 1145494
.
<pre>

The left side is  {{{2^n*x}}}.


The right side is  {{{2^10*500}}} = {{{2^10*5*100}}} = {{{2^12*5^3}}}.


Then, comparing the left and the right sides, you get <U>several solutions</U> in integer numbers:


    n = 12,  x = {{{5^3}}} = 125,

    n = 11,  x       = 250,

    n = 10,  x       = 500,

    n =  9,  x       = 1000,

    n =  8,  x       = 2000,
      
    n =  7,  x       = 4000,

    . . . .  and so on . . .  


    n =  0,  x        = {{{2^0*(2^12*5^3)}}}.
</pre>

Solved, answered, explained and completed.