f(X) = Y = X^XIf I have the equation of X raised to the power of X is Y, how do I calculate X if I am given Y?
If Y=10, I can find X via trial and error to be 2.5061841456 (discounting rounding errors). I would like a formula to work it backwards.The answer is maybe you can't find x for some y.
If y= 4, then x=2
If y = 27, then x=3
The last line of response #2 should be corrected as shown above (↑).What is the domain of f(X) (given or implied) → consequently what is the RANGE of f(X)?
The domain for both X & Y are positive numbers greater than zero. Sorry for the delay in replies but as a new member my posts need to be approved before you can see them.f(X) = Y = X^X
What is the domain of f(X) (given or implied) → consequently what is the domain of f(X)?
For these types of functions, I d not know of any simple algebraic method to solve for 'x' (exactly) - as inverse of the given function. The only way I can suggest is to use graphical method or numerical method to approximate the solution.f(X) = Y = X^X
This can't be done using elementary functions.If I have the equation of X raised to the power of X is Y, how do I calculate X if I am given Y?
Not quite. Did you not read answer #8??Am I understanding correctly that the only way to solve this problem is by trial and error zeroing in on the correct number? There's no formula to find X when given Y?
Did you not read my earlier post (#3). It is easily seen that if y=4, then x=2 (no zeroing in!). If y=27, then x=3 immediately. I used no formula and did not zero in to get my answer. Now I never said that for all values of y you can get an immediate answer. You on the other hand said that the only way to solve this problem is by trial and error--that is not always true.Am I understanding correctly that the only way to solve this problem is by trial and error zeroing in on the correct number? There's no formula to find X when given Y?
So your method in this case is not "trial and error", but "trial and success", better known as "solving by inspection".It is easily seen that if y=4, then x=2 (no zeroing in!). If y=27, then x=3 immediately.
Did you mean to say, "you can"? If that's a typo, it certainly made it harder to follow your thinking.The answer is maybe you can't find x for some y.
If y= 4, then x=2
If y = 27, then x=3