SOLUTION:  4^x - (17 times 2^x) + 16 = 0 (let me read it to make sure: 4 raised to the x power minus 17 times 2 raised to the x power plus 16 equals zero).

Algebra ->  Test -> SOLUTION:  4^x - (17 times 2^x) + 16 = 0 (let me read it to make sure: 4 raised to the x power minus 17 times 2 raised to the x power plus 16 equals zero).      Log On


   



Question 598261:  4^x - (17 times 2^x) + 16 = 0 (let me read it to make sure: 4 raised to the x power minus 17 times 2 raised to the x power plus 16 equals zero).
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
4%5Ex+-+17%282%5Ex%29+%2B+16 = 0
4 = 2 squared, therefore we can write it
2%5E%282x%29+-+17%282%5Ex%29+%2B+16 = 0
This looks like a quadratic equation where 2^x takes the place of x, factors to:
%282%5Ex+-+16%29%282%5Ex+-1%29 = 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%5E4+-+17%282%5E4%29+%2B+16 = 0
256 - 17(16) + 16 =
256 - 272 + 16 = 0
:
Do the same for x=0