solve for x: x^x^x =2^(2048) by using lambert function


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Question Number 183769 by Michaelfaraday last updated on 29/Dec/22

$s o l v e f o r x :$ $x^{x^{x}} = 2^{2048}$ $b y u s i n g l a m b e r t f u n c t i o n$
Commented by mr W last updated on 30/Dec/22

$i t h a s n o s o l u t i o n b y l a m b e r t!$ $n o s o l u t i o n b y a n y t h i n g!$
Commented by mr W last updated on 30/Dec/22

$4^{4^{4}} = 2^{512} < 2^{2048}$ $5^{5^{5}} = 5^{3125} > 2^{2048}$ $\Rightarrow t h e r o o t o f x^{x^{x}} = 2^{2048} l i e s b e t w e e n$ $4 a n d 5 .$
Commented by Michaelfaraday last updated on 30/Dec/22

$o k a y t h a n k s s i r$
Commented by paul2222 last updated on 03/Jan/23

$we can use newton raphson iteration$
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