Find the number of solutions to x^2 = 2^x.
I think the answer is 2 solutions...2 and 4 but I am unsure if there are any more.
2007-12-03 12:57:19 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
This is much easier to see if you are able to use a graphing calculator and graph the functions.
0 is not a solution because 2^0 = 1 and 0^2 = 0
starting at the y axis: The graph of 2^x intersects the y axis at 1 and opens upward sharply to the right. From the y axis going left, the graph of 2^x flattens out because negative exponents in this case are expressed as 1/2^x.
The graph of x^2 is a parabola that opens upward with its vertex at the origin.
By tracing the intersection of the graphs on a graphing calculator you will wind that there are 2 solutions:
one at ( -.7666, .5876) and (2,2) Although the fractions go on for several more decimal places before they are exact.
2007-12-03 14:00:57 · answer #1 · answered by Anonymous · 0⤊ 0⤋
it is 0 and 2, 4 is not a solution 4^2 = 16, 2x4 = 8
2007-12-03 13:02:30 · answer #2 · answered by norman 7 · 0⤊ 0⤋