Asked by STEVIUM
2 exponent x=144 base x find x,the answer is 6,but i cant figure out the workings
Answers
Answered by
Steve
You want a power of two to be
x^2+4x+4 = (x+2)^2
So, which powers of 2 are perfect squares? There are lots of answers:
(6+2)^2 = 64 = 6^2 + 4*6 + 4 = 144<sub><sub>6</sub></sub> = 2^6
(14+2)^2 = 256 = 144<sub><sub>14</sub></sub> = 2^8
All even powers of 2 are perfect squares.
x^2+4x+4 = (x+2)^2
So, which powers of 2 are perfect squares? There are lots of answers:
(6+2)^2 = 64 = 6^2 + 4*6 + 4 = 144<sub><sub>6</sub></sub> = 2^6
(14+2)^2 = 256 = 144<sub><sub>14</sub></sub> = 2^8
All even powers of 2 are perfect squares.