Solve-for-x-x-x-x-x-4-

Question Number 17989 by alex041103 last updated on 13/Jul/17

S o l v e f o r x

x^{x^{x^{x^{\dots .}}}} = 4

Commented by alex041103 last updated on 13/Jul/17

j u s t f o r f u n

Commented by mrW1 last updated on 13/Jul/17

x^{4} = 4

x =^{4} \sqrt{4} = \sqrt{2}

Commented by alex041103 last updated on 13/Jul/17

g o o d

Commented by mrW1 last updated on 13/Jul/17

{(\sqrt{2})}^{{(\sqrt{2})}^{{(\sqrt{2})}^{(\dots . .)}}} = ?

Commented by mrW1 last updated on 13/Jul/17

2^{\frac{k}{2}} = k

\Rightarrow k = 2 or 4

i . e .

{(\sqrt{2})}^{{(\sqrt{2})}^{{(\sqrt{2})}^{(\dots)}}} = 2 or 4

but how can it be two different values ?

Commented by alex041103 last updated on 13/Jul/17

a l s o - \sqrt{2} i a s o l u t i o n

{(- \sqrt{2})}^{4} = {(- 1)}^{4} {(\sqrt{2})}^{4} = 4

Commented by prakash jain last updated on 13/Jul/17

x^{x^{x^{\iddots \infty}}} = 4

\sqrt{2} is not a valid solution .

Commented by alex041103 last updated on 13/Jul/17

T r u e