What is the Solution to the Equation 2x = x^2?

[I Like Pi]

Homework Statement

solve 2^x = x²

Homework Equations

The Attempt at a Solution

i have no clue

 

[tommowg]

x = 2

 

[I Like Pi]

x = 2

how do you solve it algebraically tho

 

[p21bass]

Try using logs.

 

[I Like Pi]

Try using logs.

i get xlogx = 2log2

 

[p21bass]

No - that's wrong. You seem to have divided where you should have multiplied.

 

[Apphysicist]

x = 2

But that is not the only answer.

I'm not sure you can solve this with simple algebra though. Using fractional exponents or logs may make it easier to look at with x's on one side, but not necessary solvable.

 

[Mark44]

I agree with Apphysicist. There is no simple way to solve for x analytically in this equation.

 

[Dickfore]

There are 3 solutions in the set of real numbers:

x = 2 is surely a solution;

The other two are in the intervals:

x > e and

-1 < x < 0

 

[JonF]

Your teacher / book probably just wants you to give 2 as an answer. Other answers would be in terms of something like the Lambert W Function, which is something you wouldn't even know exists until you've had a few more years of math.

 

[gerimis]

m.wolframalpha.com/input/?i=%32^x%20%3d%20x%c2%b2&x=0&y=0

x = 2
x = 4

 

[Dickfore]

Another approximate solution is:

$$x \approx -0.7666646959621232$$