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Homework Help: Is this possible to solve?

  1. Apr 1, 2008 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant 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?
     
  2. jcsd
  3. Apr 1, 2008 #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.
     
  4. Apr 1, 2008 #3
    Ok, thank you.
     
  5. Apr 1, 2008 #4
    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] ??
     
  6. Apr 2, 2008 #5
    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].
     
  7. Apr 2, 2008 #6
    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]
    .
     
  8. Apr 2, 2008 #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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