SOLUTION: show that for t>0, log (t) is not a polynaomial. I understand what a logarithm is now but it still doesn't help me here.

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Question 4732: show that for t>0, log (t) is not a polynaomial. I understand what a logarithm is now but it still doesn't help me here.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Define f(t) = log(t) is a function.

Claim: f is not a polynomial in t.
Supppose f were not a polynomial in t of degree n.
then the derivative f' is a polynomial in t of degree n-1.
But, f'(t) = 1/(t ln10) (where ln is the natural logarithm) is
not a polynomial.
This shows f' and so f cannot be a polynomial in t.
Kenny