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Question Number 167966 by mathlove last updated on 30/Mar/22

Answered by HeferH last updated on 30/Mar/22

$$x^{x^4}=4$$$${\left(x^{x^4}\right)}^4={\left(4\right)}^4$$$${\left(x^4\right)}^{x^4}=4^4$$$$x^4=4$$$$x=\sqrt[4]{4}$$$$x={\left(2^2\right)}^{\frac{1}{4}}\to 2^{\frac{1}{2}}$$$$x=\sqrt{2}$$$${\left(\sqrt{2}\right)}^{{\left(\sqrt{2}\right)}^8}+{\left(\sqrt{2}\right)}^{{\left(\sqrt{2}\right)}^2}={\left(2^{\frac{1}{2}}\right)}^{16}+{\left(2^{\frac{1}{2}}\right)}^2$$$${\left(2^{\frac{1}{2}}\right)}^{16}+{\left(2^{\frac{1}{2}}\right)}^2=2^8+2=258$$$$$$

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