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Nonlinear Functions

SAT Math· difficulty 5/5

For very large xx, which inequality is true?

  • A

    1.5x>x101.5^x > x^{10}

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  • B

    x>log⁡x\sqrt{x} > \log x

  • C

    x10=1.5xx^{10} = 1.5^x

  • D

    x10>1.5xx^{10} > 1.5^x

Explanation

Any exponential with base >1> 1 eventually exceeds any polynomial.

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