Is there an x such that e^x = 0?

  • Thread starter punjabi_monster
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In summary, the conversation discusses the possibility of e^x being equal to 0 and for what values of x this may occur. It is concluded that e^x can never actually equal 0, but it approaches 0 as x approaches negative infinity. The graph of e^x is also mentioned as a helpful visual aid in understanding this concept.
  • #1
punjabi_monster
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hi,
i have a question. :uhh:

e^x =0
is this possible, and for what values of x if so.?
 
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  • #2
No.

If you understand the idea of limits you can say that e^x approaches 0 as x approaches negative infinity

[tex]\lim_{\substack{x \rightarrow - \infty\\}} e^x = 0 [/tex]

The larger and larger negative numbers you get for x, the closer and closer to zero you will get for e^x. But you can never actually get 0.

~Lyuokdea
 
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  • #3
For more help, you can draw the graph of [itex]e^x[/itex] , the graph is an increasing function and which approaches zero and -infinity, but never equals zero.

BJ
 
  • #4
yes i see. thank-you for your help.
 

1. What is the value of x when e^x = 0?

The value of x cannot be determined because the exponential function e^x does not have a solution for 0.

2. Is there any number that can be substituted for x to make e^x equal to 0?

No, there is no real number that can be substituted for x to make e^x equal to 0. The exponential function e^x is always positive and never equals 0.

3. What does the graph of e^x = 0 look like?

The graph of e^x = 0 does not exist because there is no solution for this equation. The graph of the exponential function e^x is always positive and never crosses the x-axis.

4. Can complex numbers be used to solve e^x = 0?

Yes, complex numbers can be used to solve e^x = 0. The solution is x = 0 + 2πni, where n is any integer and i is the imaginary unit.

5. Why is there no solution for e^x = 0?

This is because the exponential function e^x is defined as the limit of (1+x/n)^n as n approaches infinity. This limit is always positive and never equals 0, therefore there is no solution for e^x = 0.

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