Math expert need to solve simple problem

[John Fitzpatrick]

An easy algebra problem is, given Y=X^2 (Y equals X squared) solve for X. The answer, as any modern Major General knows, is: X= +/- Y^.5 (X equals plus or minus the square root of Y).

So, can any math major out there tell me why this simple equation has no solution for X as a function of Y? Y=X^X. I've played around with it for years but get no where.

 

[Jeff Young]

I'd just sue.

 

[Ian K]

An easy algebra problem is, given Y=X^2 (Y equals X squared) solve for X. The answer, as any modern Major General knows, is: X= +/- Y^.5 (X equals plus or minus the square root of Y).

So, can any math major out there tell me why this simple equation has no solution for X as a function of Y? Y=X^X. I've played around with it for years but get no where.

Because the inverse functions are logarithmic functions.

Y=X^X

becomes

ln(Y) = X*ln(X) for X > 0

which, solving for X yields

X = [ ln(Y) ]/[ ln(X) ] for X > 0

and there is no way to isolate the X without getting back to the original equation, or using Euhler's number, but that would still give you something like X * e^X, which doesn't help.

At least says my rusty math ...

Ian

 

[Ron Earp]

I think because you're using a transcendental function.

Transcendental function - Wikipedia, the free encyclopedia

Which means you can't express it in a finite series of algebraic expressions. Others like this are trig expressions, sin, cos, tan, etc.

X^4 is expressed X * X * X * X

But X^X, you're SOL.