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Question Number 186690 by mathlove last updated on 08/Feb/23

Answered by a.lgnaoui last updated on 08/Feb/23

$$\mathrm{x}\times 2^{{\mathrm{x}}^2}=4(\mathrm{x}={\mathrm{a}}^2)$$$${\mathrm{x}}^2\times 2^{{\mathrm{x}}^2}=4\mathrm{x}$$$$\mathrm{posons}\mathrm{x}=\mathrm{z}$$$$\mathrm{z}\times 2^{\mathrm{z}}=2^2\mathrm{z}$$$$\mathrm{logz}+\mathrm{zlog}2=2\log 2+\mathrm{logz}$$$$\mathrm{zlog}2=2\log 2$$$$\mathrm{z}=2$$$${\mathrm{x}}^2=2={\left({\mathrm{a}}^2\right)}^2\Rightarrow a^2=\sqrt{2}$$$$a{=}^4\sqrt{2}$$$$$$

Commented by mr W last updated on 08/Feb/23

$$wrongagain!$$$$manyerrors!$$$$a^a\ne a^2$$$$a^{a^2}=a^{a\times a}={\left(a^a\right)}^a\ne {\left(a^a\right)}^2$$

Commented by aba last updated on 08/Feb/23

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{correct}$$

Commented by aba last updated on 08/Feb/23

$$\mathrm{he}\mathrm{posed}\mathrm{x}={\mathrm{a}}^{\mathrm{a}}$$

Commented by aba last updated on 08/Feb/23

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Commented by mr W last updated on 08/Feb/23

$$wheredidyoustudymathematicssir?$$$$2^{a^{a^2}}\ne 2^{{\left(a^a\right)}^2}$$$$trythis:$$$$3^{3^2}=3^9=19683$$$${\left(3^3\right)}^2={27}^2=729$$

Commented by aba last updated on 08/Feb/23

$$\mathrm{oh}\mathrm{ok}\mathrm{i}\mathrm{see}.\mathrm{You}\mathrm{are}\mathrm{right}$$$$\mathrm{sorry}$$

Commented by mr W last updated on 08/Feb/23

$$alrightsir!$$

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