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4 solutions
Let b b b . . . = x b ( b b ) . . . = x 2 b ( x ) = x 2 b = x
good question
much more based on s u m u p t o i n f i n i t y
(b^1 /2)b^1 /4)b^1 /8)b^1 /16)...... =b^(1/2+1/4+1/8+........) =b^1 =b,since 1+x+x^2+x^3+.....=1
Can be simplified to b^(1/2) b^!1/4) b^(1/8).... =b^(1/2 + 1/4 + 1/8+...) = b^[(1/2)/(1-1/2)] by sum to infinity = b^1.
Let √b√√b√√√b ... = x
Then X^2 = b√b√√b...
Therefore x^2/x = x = b√b√√b / √b√√b√√√b = b
Therefore x = b
Refer to image