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(C) To find the number of solutions for the equation $2^x = x^2$, we can analyze the intersection points of the functions $f(x) = 2^x$ and $g(x) = x^2

Vedclass · Accepted Answer

$3$

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(C) To find the number of solutions for the equation $2^x = x^2$, we can analyze the intersection points of the functions $f(x) = 2^x$ and $g(x) = x^2$.$1$. For $x $2$. For $x > 0$: We check specific integer values:At $x = 2$, $2^2 = 4$ and $2^2 = 4$. So, $x = 2$ is a solution.At $x = 4$, $2^4 = 16$ and $4^2 = 16$. So, $x = 4$ is a solution.$3$. Between $x = 2$ and $x = 4$, the function $x^2$ is greater than $2^x$ (e.g., at $x = 3$, $2^3 = 8$ and $3^2 = 9$).For $x > 4$, the exponential function $2^x$ grows much faster than the quadratic function $x^2$, so there are no more solutions for $x > 4$.Thus, the solutions are $x = -0.766$ (approx), $x = 2$, and $x = 4$. There are a total of $3$ solutions.

The number of solutions of the equation $2^x = x^2$ is

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