A variable raised to a power that contains that variable, all equal to one?

I put the following problem into Wolfram Alpha and found that the solutions are the square root of e and 1. Can somebody explain how you'd solve it to get both of those answers? I only got the square root of e. Here's the problem:

x^(ln(x) - 0.5) = 1

It makes sense to me that 1 works as well, but am I missing some kind of rule that would have made me get 1 when I solved it the first time around?

Re: A variable raised to a power that contains that variable, all equal to one?

Quote:

Originally Posted by

**MRich520** x^(ln(x) - 0.5) = 1

I am glad that works for you.

Now do you agree that

If you do then what does

Re: A variable raised to a power that contains that variable, all equal to one?

Quote:

Originally Posted by

**Plato** I am glad that

works for you.

Now do you agree that

If you do then what does

Eh...I'm not sure if that was the answer you were asking for. Mind clarifying?

Re: A variable raised to a power that contains that variable, all equal to one?

Quote:

Originally Posted by

**MRich520**
Eh...I'm not sure if that was the answer you were asking for. Mind clarifying?

Well what is

And what is to that power?

Re: A variable raised to a power that contains that variable, all equal to one?

Hello, MRich520!

Take logs: .

We have: .

And we have two equations to solve:

. .

Re: A variable raised to a power that contains that variable, all equal to one?

Thanks!

I should know that from my classes :p.

And sorry Plato I forgot to respond :(