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Question Number 87773 by john santu last updated on 06/Apr/20

$${}^3\log \left({}^{{\mathrm{x}}^2}\log \left({}^{{\mathrm{x}}^2}\log {\mathrm{x}}^4\right)\right)>0$$

Commented by john santu last updated on 06/Apr/20

$$\Rightarrow {}^{{\mathrm{x}}^2}\log \left({}^{{\mathrm{x}}^2}\log {\mathrm{x}}^4\right)>1$$$$\left(\mathrm{i}\right)\mathrm{x}\ne 0$$$$\left(\mathrm{ii}\right){}^{{\mathrm{x}}^2}\log \left({}^{{\mathrm{x}}^2}\log {\mathrm{x}}^4\right)>{}^{{\mathrm{x}}^2}\log {\mathrm{x}}^2$$$$\Rightarrow ({\mathrm{x}}^2-1)({\mathrm{x}}^4-{\mathrm{x}}^2)>0$$$${(\mathrm{x}+1)}^2{(\mathrm{x}-1)}^2{\mathrm{x}}^2>0$$$$\mathrm{x}\ne -1,\mathrm{x}\ne 1$$$$\left(\mathrm{iii}\right)1<{\mathrm{x}}^2<2\{\begin{array}{l}-\sqrt{2}<\mathrm{x}<-1\\ 1<\mathrm{x}<\sqrt{2}\end{array}$$

Commented by mahdi last updated on 06/Apr/20

$$\mathrm{what}\mathrm{meaning}\left({\mathrm{x}}^2\right)\mathrm{in}\stackrel{{\mathrm{x}}^2}{}\log ?$$$$$$

Commented by john santu last updated on 06/Apr/20

$$\mathrm{it}\mathrm{same}\mathrm{to}{\log }_{{\mathrm{x}}^2}\left({\mathrm{x}}^4\right)$$

Commented by mahdi last updated on 06/Apr/20

$$\mathrm{thanks}$$

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