Question 598261
{{{4^x - 17(2^x) + 16}}} = 0
4 = 2 squared, therefore we can write it
{{{2^(2x) - 17(2^x) + 16}}} = 0
This looks like a quadratic equation where 2^x takes the place of x, factors to:
{{{(2^x - 16)(2^x -1)}}} = 0
Two solutions
2^x = 1
2^0 = 1
therefore 
x = 0
and
2^x = 16
2^4 = 16
therefore
x = 4
:
Check this by replacing x with 4 in the original equation
{{{4^4 - 17(2^4) + 16}}} = 0
256 - 17(16) + 16 =
256 - 272 + 16 = 0
:
Do the same for x=0