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Give a Big-Oh Estimate for (x-7)log(x3+4x+1) + 3x7. Please break down steps used. I am mostly...

Give a Big-Oh Estimate for (x-7)log(x3+4x+1) + 3x7.

Please break down steps used. I am mostly unsure how to address the log.

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Answer #1

(x-7)log(x^3+4x+1) + 3x^7
<=  (x-7)log(x^4) + 3x^7    (because x^3+4x+1 < x^4)
=   4(x-7)log(x) + 3x^7   (because log(x^4) = 4 log(x))
ignore constant terms
=    xlog(x) + x^7
=   O(x^7)  (because xlog(x) < x^7)

Answer: O(x^7)
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