anonymous 5 years ago Show that for t>0 logt is not a polynomial.

1. amistre64

umm.. it doesnt fit the definition of a poly maybe?

2. anonymous

what is the definition of log(t)?

3. amistre64

4. anonymous

has only one zero? hard to know what this question is asking

5. anonymous

amistre i have a question for you. solve for x: 3x+1

6. anonymous

u have o prove that its not a polynomial...thats what given in my book's exercise..

7. amistre64

they always say proving a negative cant be done

8. anonymous

still not sure what it is asking. you need some definition to work with. presumably you are supposed to use some property of the logs that polynomials don't have, but there are so many

9. amistre64

arent logs exponents?

10. anonymous

May be a polynomial is something which has only terms like ax^b

11. anonymous

ln(ab)=ln(a)+ln(b) for example. what polynomial has that property?

12. anonymous

u have to prove it rigourously..

13. amistre64

define rigorous lol

14. anonymous

well you cannot prove it rigorously without appealing to a definition is my guess.

15. anonymous

means the math teacher likes it.

16. anonymous

Yes, you can't say that an apple is red, or is not orange, without defining what red and orange are!

17. anonymous

no polynomial has a vertical asymptote. no polynomial is undefined at 0.

18. anonymous

i said t>0 satellite73

19. anonymous

so? still any asymptote yes? limit as x->0 ln(x) = - infinity

20. anonymous

use this definition:In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

21. anonymous

no poly has that property.

22. anonymous

prove that no polynomial has that property..

23. anonymous

???

24. anonymous

well its easy

25. anonymous

k. accepted..but would like noncalculus proof..

26. anonymous

the more i think about this the less sense it makes. i am not really sure what it is after. probably something along the lines of "sin(x) is not a polynomial because a polynomial of degree n has at most n real zeros"

27. anonymous

so probably some property of the logs that polynomials do not possess. already suggested ln(ab)=ln(a)+ln(b)

28. anonymous

well deriving from the main definition is the job..

29. anonymous

the book told so..

30. anonymous

i think all the properties will come from the definition.

31. anonymous

but f(xy)=f(x)+f(y) may be true for some polynomials..

32. anonymous

so tat property cant be used!!!

33. anonymous

f(xy)=f(x)+f(y) is not true for any polynomial.

34. anonymous

well f(2x)=constant+f(x) does not hold for any polynomial but with log

35. watchmath

With calculus: Suppose it is equal to some $$p(t)$$ then $$\lim_{t\to \infty} \log t/p(t)=1$$ On the other hand, by L'hospital rule $$\lim \log t/p(t)=0$$

36. anonymous

@amogh what about the zero polynomials?

37. anonymous

what is with the latex?

38. anonymous

its screwed up...

39. anonymous

I don't think constants come into polynomials, do they?