- #1
3hlang
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i know this is possible to find with iteration, but is it possible to find it algebraically?
If y=x^x then what is x in terms of y?
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In summary, the conversation discusses finding a solution for the equation x=y^y through algebraic means. The concept of using the Lambert W function as an inverse for xln(x) is mentioned, and the idea of swapping x and y in the equation is also brought up. The question of what the W function is of is asked, but the conversation does not provide a clear answer.
- #2
tiny-tim
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Hi 3hlang! 
Nope!
3hlang said:
Nope!
- #3
HallsofIvy
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This probably isn't what you mean by "algebraically" but if you take the logarithm of both sides of the equation you get ln(y)= xln(x) and then x= W(ln(y)) where W is the "Lambert W function" which is defined as the inverse function to xln(x).
- #4
g_edgar
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... and the reason we talk about the Lambert W function is that none of the previously-defined standard functions would work.
- #5
3hlang
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so if x=y^y, then y=?
- #6
HallsofIvy
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3hlang said:
HallsofIvy said:
All you have done is swap x and y! If [itex]x= y^y[/itex] then, by the same formula I gave before, y= W(ln(x)).
- #7
3hlang
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what? i wasn't claiming to have done anything radical to the formula. all i wanted to know was what you do the w function of. but thank you for telling me
FAQ: If y=x^x then what is x in terms of y?
What is the value of x when y is given in the equation y=x^x?
The value of x cannot be determined exactly when y is given in the equation y=x^x. This is because there are infinite possible values of x that can satisfy the equation.
How can the value of x be calculated if y is known in the equation y=x^x?
The value of x can be approximated using numerical methods such as trial and error or by using a graphing calculator to find the point of intersection between the curve y=x^x and the line y=y. However, there is no exact formula to calculate the value of x in terms of y.
Is there a way to solve for x algebraically in the equation y=x^x?
No, there is no algebraic method to solve for x in terms of y in the equation y=x^x. This is because the equation involves both x and y as exponents, making it impossible to isolate x on one side of the equation.
Can the equation y=x^x be rewritten to solve for x in terms of y?
No, the equation y=x^x cannot be rewritten to solve for x in terms of y. This is because the equation involves both x and y as exponents, making it impossible to isolate x on one side of the equation.
Why is it not possible to determine the value of x in terms of y in the equation y=x^x?
It is not possible to determine the value of x in terms of y in the equation y=x^x because there are infinite possible values of x that can satisfy the equation. Additionally, the equation involves both x and y as exponents, making it impossible to isolate x on one side of the equation.