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Anonymous Fri 06 Sep 17:28:42 2019 No.10949478 View Reply Original Report

Quoted By: >>10949483 >>10949495

Prove that the quotient of a^(f(x)) and b^(g(x)) is never a polynomial if a=/=b.

Anonymous

Anonymous Fri 06 Sep 2019 17:30:09 No.10949483 Report

Quoted By: >>10949505

>>10949478
Holy shit, I forgot the most important bit.
>When f and g are both elementary functions.

Anonymous

Anonymous Fri 06 Sep 2019 17:34:22 No.10949495 Report

Quoted By: >>10949505 >>10949542 >>10949594

>>10949478
It can be though. For example a=10, f(x)= log x^3, b=e, g(x)=ln x yields a^(f(x))/(b^(g(x)))=x^2

Anonymous

Anonymous Fri 06 Sep 2019 17:37:31 No.10949505 Report

Quoted By:

>>10949483
>>10949495
Oh, well then because exponentiation, unless you count polynomials of degree 0 or 1

Anonymous

Anonymous Fri 06 Sep 2019 17:45:54 No.10949527 Report

Quoted By: >>10949536

false.

f(x) = 0
g(x) = 0
(constant functions are elementary functions)

a ^ (F(x)) / b ^ (g(x)) = 1, which is a polynomial.

OP Fri 06 Sep 2019 17:49:33 No.10949536 Report

Quoted By: >>10949542

>>10949527
This question was posed to me by a friend who knows more math than me; they've clarified they mean of degree 2 or higher.

Anonymous

Anonymous Fri 06 Sep 2019 17:51:56 No.10949542 Report

Quoted By: >>10949554

>>10949536
what's wrong with this (dis)proof then? >>10949495

Anonymous

Anonymous Fri 06 Sep 2019 17:56:23 No.10949554 Report

Quoted By: >>10949560

>>10949542
The elementary functions bit. Shit's dumb

Anonymous

Anonymous Fri 06 Sep 2019 17:59:29 No.10949560 Report

Quoted By: >>10949594

>>10949554
but anon, logarithms are elementary functions
https://en.wikipedia.org/wiki/Elementary_function#Basic_examples

Anonymous

Anonymous Fri 06 Sep 2019 18:12:18 No.10949594 Report

Quoted By:

>>10949560
Oh really? Wow, I'm fucking dumb.

Hey OP, I got it in one and apparently I'm a complete fucking moron. Tell your friend to put that in his pipe and smoke it.
>>10949495

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