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Is this possible to solve?

  • #1
1. Homework Statement

[tex]{3}^{tg2x}*{3}^{ctg3x}=0[/tex]

2. Homework Equations



3. The Attempt at a Solution

Is this possible to solve?

I don't think so.

[tex]{3}^{tg2x+ctg3x}=0[/tex]

For whatever value of x, we can't get 0, right?
 

Answers and Replies

  • #2
HallsofIvy
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you are correct. No value of x will make [itex]3^x= 0[/itex] so that equation has no solution.
 
  • #3
Ok, thank you.
 
  • #4
1,631
4
you are correct. No value of x will make [itex]3^x= 0[/itex] so that equation has no solution.
If we suppose that x is from the extended reals [tex]x\in[-\infty,+\infty][/tex],

Could we say then that equations like [tex] a^{x}=0[/tex] have solution for [tex]x=-\infty, \ \ \ a\in R[/tex] ??
 
  • #5
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It is true that [tex]\lim_{x\to-\infty}a^x = 0[/tex] when |a| > 1, but that is not the same as saying that [itex]x = -\infty[/itex].
 
  • #6
1,631
4
It is true that [tex]\lim_{x\to-\infty}a^x = 0[/tex] when |a| > 1, but that is not the same as saying that [itex]x = -\infty[/itex].
Yeah, i do understand this part, i was just wondering how does one perform opertations on the extended reals, that is [tex][-\infty,+\infty][/tex], rather than just in [tex](-\infty,+\infty)[/tex]
.
 
  • #7
HallsofIvy
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I'm not aware of any way of way of definining trig functions on the extended reals.
 

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