SOLUTION: This question talks about how the sqrt of x is to the exponent of sqrt of x indefinitely. The answer to it is 2 but the goal is to find x. How would you solve this question? Ima

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Question 1134981: This question talks about how the sqrt of x is to the exponent of sqrt of x indefinitely. The answer to it is 2 but the goal is to find x. How would you solve this question?
Image : https://ibb.co/pdHnWmt''.
I don’t get how it’s 2. Please explain a method without involving graphing calculator.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Previously answered (question 1134770); the response is repeated here.

Given: sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)... = 2

Square both sides, remembering that

sqrt(x)^(2*sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)...) = 4

sqrt(x)^(2*2) = 4 [everything after the 2 in that equation is equal to what we started with; its value is 2]

sqrt(x)^4 = 4

x^2 = 4

x = 2

The result can be verified using excel, or a graphing calculator.

(1) Calculate the square root of 2;
(2) calculate the square root of 2 raised to that power;
repeat step (2) repeatedly
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.


Given :  sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)... = 2.    (1)



Look into the many-floor degree index at the lowest  .


This  many-floor degree index is nothing else as 2 (as it is given !).


So you can rewrite equation (1) in an equivalent form


     = 2.     (2)


Since   = x,   equation (2) is equivalent to


    x = 2,    which gives you the ANSWER.

Solved.


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