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This isn't so easy. Start by restating it with mathematical symbols:
x^2 > 2^x
Since both sides are positive numbers, it's okay to take the log of both sides (ln = natural log) and preserve the inequality.
ln (x^2) > ln(2^x)
which can be re-written:
2 ln x > x ln 2
(ln x)/x > (ln 2)/2 =~ 0.34657359028...
It looks like the function maxes out to a value of 1/e = 0.36...
So there's a small range of x values containing e where the inequality is true. The endpoints of this interval are found by making it an equation instead of inequality.
I'm not sure this can be solved in closed form. Normally numerical (computer approximation) would be used, I think.
The lesson to be learned, however, is that an exponential function will eventually overtake any power function of x.
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∙ 11y ago
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What are a carpet's dimensions if one side of the carpet is seven meters shorter than the length and the diagonal is one meter longer than the length?
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How do you calculate the height of a right triangle given the base length and all three angles?
if you have a regular triangle u have to use the paythagorem theory A squared plus b squared equals c squared and than u have to take half the base of the triangle and the number of one of the sides and substitute into the equation and solve the b squared should be the height of ur triangle :)
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