zero of the polynomial
3a-2
please solve this
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Answer:
please write it in brief
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I'm assuming the question is meant to read:
10n≤n10
Python tells us:
>>> [n for n in range(1,100) if 10**n <= n**10]
[2, 3, 4, 5, 6, 7, 8, 9,10]
>>> len([n for n in range(1,100) if 10**n <= n**10])
9
But to actually think it out without Python-bashing:
1 doesn't grow from exponents, so 110 won't be bigger than 101 . We start at n=2 .
On the positive integers, both sides are strictly increasing, and we know the left side of the equation grows strictly faster than the right side, so once the left side is greater, it will remain greater.
At n=10 , we get 1010≤1010 .
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