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if x to power x to power x......upto infinity = 2 then find x...............I got my ans as (underroot 2)............but if I change the value from 2 to 4 or 6 or 8 ...............the ans is same ------(underroot 2).......the answer is both correct and wrong.........how is it possible???? see how i got my ans---- let x to power x to power x......upto infinity = y then x to power y = y ...................................... y = 2................................ x squre = 2.......................................................... x = uderoot 2 PLS CORRECT ME IF I AM WRONG!!!!! THE QUESTION IS--------- x^x^x^x.......∞ = 2

if x to power x to power x......upto infinity = 2 then find x...............I got my ans as (underroot 2)............but if I change the value from 2 to 4 or 6 or 8 ...............the ans is same ------(underroot 2).......the answer is both correct and wrong.........how is it possible???? see how i got my ans---- let x to power x to power x......upto infinity = y then x to power  y =   y  ...................................... y = 2................................ x squre = 2.......................................................... x = uderoot 2 PLS CORRECT ME IF I AM WRONG!!!!! 
                                                    THE QUESTION IS---------


 

  x^x^x^x.......∞ = 2

Grade:9

2 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

for all x>1, x^x^x^x...∞→∞,therefore your method of solution technically breaks down. This is like, for example, the formula

1+x+x^2+x^3...∞ =(1/(1-x)) breaks down when lxl ≥1 

Akshay Malik
16 Points
9 years ago

see if you replace 2 by 6, the the answer is not root 2 but 6th root of 6.. and this is the only approach to this. You are absolutely correct.

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