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The two are equal at three points: x = -0.766 664 7.., x = 2 and x = 4.

For x < -0.766 644 7.., x2 is greater

For -0.766 644 7.. < x < 2, 2x is greater

For 2 < x < 4, x2 is greater

For 4 < x, 2x is greater

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Q: Is 2 by the power of x greater than x by the power of 2?
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