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Combination

Number of rea...

Question

Number of real solution(s) of $x^{x^{x^{x^{\dots}}}} = 3$ is

A

0

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B

1

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C

2

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D

3

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Solution

The correct option is B $1$
$x^{x^{x^{x^{\dots}}}} = 3$
$\Rightarrow x^{3} = 3$
$\Rightarrow x = 3^{1 / 3}$
Only one real solution.

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