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October 27th, 2018, 12:09 PM   #1
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e^n

Is the next sentence true or false:

Every e^(number) equations are transcendental equation.
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October 27th, 2018, 12:19 PM   #2
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I wouldn't say that $e^0 = 1$ is transcendental.
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October 27th, 2018, 12:32 PM   #3
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Quote:
Originally Posted by romsek View Post
I wouldn't say that $e^0 = 1$ is transcendental.
O.K.
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is this sentence true/false:
every e^(complex number) is transcendental?
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October 27th, 2018, 12:33 PM   #4
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Quote:
Originally Posted by shaharhada View Post
O.K.
thanks.

is this sentence true/false:
every e^(complex number) is transcendental?
How dare you ask this question right after quoting and thanking his post that you obviously didn't read????
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October 27th, 2018, 12:47 PM   #5
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Quote:
Originally Posted by Micrm@ss View Post
How dare you ask this question right after quoting and thanking his post that you obviously didn't read????
Sorry, but I don't understand.
I ask on other thing.
The first question in about number that I don't understand if there is counterexample to the sentence...
And in second question I ask about particular thing, the complex number.

The second question is about all the complex number and my question is about counterexample of it.
So why question is:
Why it can't be a counterexample in the second question?
Is There a reason to it?
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October 27th, 2018, 01:02 PM   #6
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$e^{\ln(k)} = k,~\forall k \in \mathbb{Z},~k>0$

Do you consider this transcendental? Certainly $k$ isn't.

$\ln(k)$ however probably is
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October 27th, 2018, 01:43 PM   #7
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$e^{\ln(k)} = k,~\forall k \in \mathbb{Z},~k>0$

Do you consider this transcendental? Certainly $k$ isn't.

$\ln(k)$ however probably is
In the second question I ask about complex numbers.
Is there example of counterexample to algebraic solution to this equation?
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October 27th, 2018, 01:45 PM   #8
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In the second question I ask about complex numbers.
Is there example of counterexample to algebraic solution to this equation?
ln(k) is a complex number.
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October 27th, 2018, 02:02 PM   #9
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Originally Posted by shaharhada View Post
In the second question I ask about complex numbers.
Is there example of counterexample to algebraic solution to this equation?
I really have no idea what you are asking here.
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October 27th, 2018, 05:12 PM   #10
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Originally Posted by shaharhada View Post
Is the next sentence true or false:

Every e^(number) equations are transcendental equation.
There's a little confusion and ambiguity in your question.

First, if $n$ is a number -- integer, real, or complex -- then $e^n$ is another number. It's not an equation. So it might or might not be a transcendental number, but it's always one single, particular number. Not an equation.

We could ask when $e^n$ is transcendental. It's pretty clear that if $n$ is an integer, $e^n$ is transcendental if and only if $n$ is nonzero.

If $n$ is real, $e^n$ is transcendental unless we specifically select $n$ so it's not. For example if $n$ = $\ln 2$, then $e^n = 2$, which is not transcendental. Of course I haven't given or thought about the exact criteria by which we can know if a real exponent leads to a transcendental number. But you can always use a natural log to undo raising $e$ to a power. And vice versa. That's the most important thing to know about log and exp. They undo each other.

If $n$ is complex it's much the same. Some specifically cook-up values will give you non-transcendentals (aka algebraics) and "random" complex numbers will generally lead to transcendental complex numbers.

So that's one problem I have with your question. The way you phrased it, it refers to numbers and not equations.

Secondly, what is a transcendental equation? Do you mean it in the sense of https://en.wikipedia.org/wiki/Transcendental_equation? Or do you mean $e^z$ as a function?

So your question is ambiguous in a couple of ways and that's perhaps why you are not happy with the responses you're getting.
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Last edited by Maschke; October 27th, 2018 at 05:14 PM.
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