Solution to X^2 = 2^X: know the answer but don't know why

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Travlar

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X^2 = 2^X

I know the answer, I just don't know how to prove it mathematically. Also, I don't know if this is the right forum or not, so please be kind if its leaning towards the not :D
 
Travlar said:
X^2 = 2^X

I know the answer, I just don't know how to prove it mathematically. Also, I don't know if this is the right forum or not, so please be kind if its leaning towards the not :D
Click to expand...

Since you posted in geometry:

Plot

y = 2^x

and

y = x^2

Find the points of intersection(graphically) - there will 3 of those (x = ~ -23/30 and ther other two obvious ones)- and check.
 
X^2 = 2^X

I know the answer, I just don't know how to prove it mathematically. Also, I don't know if this is the right forum or not, so please be kind if its leaning towards the not :D
 
\(\displaystyle x^{2}=2^{x}\)

\(\displaystyle 2ln(x)=xln(2)\)

\(\displaystyle \frac{ln(x)}{x}=\frac{ln(2)}{2}\)

Now, see it?.

I assume you know the solutions are 2 and 4.
 
I know this is a duplicate post, but I was told that I posted in the wrong area.

There are actually three answers, 2, 4 and -0.7666.....

I still don't know how to get all three
 
Oh, I forgot about the third one.

I showed you how to get the first one easy enough. x=4 is easy as well from what I gave you. Use a little log laws and you have it.

As for the third one, that would probably be easiest with a graph.
 
For the third one if you can't graph, use Newton's Method. Three iterations starting at n = -.5 will give
you -.766664695962.
 
Two threads merged.

Travlar said:
I know this is a duplicate post, but I was told that I posted in the wrong area.
Click to expand...
Nobody said anything about the location being "wrong"; the tutor gave you a geometrical solution because you'd posted originally to geometry.

Eliz.
 
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