Question 1134981
<br>
Previously answered (question 1134770); the response is repeated here.<br>
Given:  sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)... = 2<br>
Square both sides, remembering that {{{(a^b)^2 = a^(2b)}}}<br>
sqrt(x)^(2*sqrt(x)^sqrt(x)^sqrt(x)^sqrt(x)...) = 4<br>
sqrt(x)^(2*2) = 4  [everything after the 2 in that equation is equal to what we started with; its value is 2]<br>
sqrt(x)^4 = 4<br>
x^2 = 4<br>
x = 2<br>
The result can be verified using excel, or a graphing calculator.<br>
(1) Calculate the square root of 2;
(2) calculate the square root of 2 raised to that power;
repeat step (2) repeatedly