# Is this possible to solve?

1. Homework Statement

$${3}^{tg2x}*{3}^{ctg3x}=0$$

2. Homework Equations

3. The Attempt at a Solution

Is this possible to solve?

I don't think so.

$${3}^{tg2x+ctg3x}=0$$

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

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HallsofIvy
Homework Helper
you are correct. No value of x will make $3^x= 0$ so that equation has no solution.

Ok, thank you.

you are correct. No value of x will make $3^x= 0$ so that equation has no solution.
If we suppose that x is from the extended reals $$x\in[-\infty,+\infty]$$,

Could we say then that equations like $$a^{x}=0$$ have solution for $$x=-\infty, \ \ \ a\in R$$ ??

It is true that $$\lim_{x\to-\infty}a^x = 0$$ when |a| > 1, but that is not the same as saying that $x = -\infty$.

It is true that $$\lim_{x\to-\infty}a^x = 0$$ when |a| > 1, but that is not the same as saying that $x = -\infty$.
Yeah, i do understand this part, i was just wondering how does one perform opertations on the extended reals, that is $$[-\infty,+\infty]$$, rather than just in $$(-\infty,+\infty)$$
.

HallsofIvy