Question

Show that for t>0 logt is not a polynomial.

Answer 1

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

Answer 2

what is the definition of log(t)?

Answer 3

gotta ask a lumberjack hah!

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

they always say proving a negative cant be done

Answer 8

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

Answer 9

arent logs exponents?

Answer 10

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

Answer 11

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

Answer 12

u have to prove it rigourously..

Answer 13

define rigorous lol

Answer 14

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

Answer 15

means the math teacher likes it.

Answer 16

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

Answer 17

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

Answer 18

i said t>0 satellite73

Answer 19

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

Answer 20

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.

Answer 21

no poly has that property.

Answer 22

prove that no polynomial has that property..

Answer 23

???

Answer 24

well its easy

Answer 25

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

Answer 26

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"

Answer 27

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

Answer 28

well deriving from the main definition is the job..

Answer 29

the book told so..

Answer 30

i think all the properties will come from the definition.

Answer 31

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

Answer 32

so tat property cant be used!!!

Answer 33

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

Answer 34

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

Answer 35

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
\(\lim \log t/p(t)=0\)

Answer 36

@amogh what about the zero polynomials?

Answer 37

what is with the latex?

Answer 38

its screwed up...

Answer 39

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