If-x-x-4-4-what-is-the-value-of-x-x-2-x-x-8-

Question Number 19785 by Tinkutara last updated on 15/Aug/17

If x^{(x^{4})} = 4, what is the value of

x^{(x^{2})} + x^{(x^{8})} ?

Answered by Tinkutara last updated on 16/Aug/17

Let x = y^{\frac{1}{4}} \Rightarrow x^{4} = y

y^{\frac{y}{4}} = 4

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

Commented by ajfour last updated on 16/Aug/17

very nice trick .

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