Question Number 190425 by 073 last updated on 02/Apr/23
Answered by mahdipoor last updated on 02/Apr/23
$${F}\left({x}\right)={sin}^{−\mathrm{1}} \left({ln}\left({log}\left({x}\right)\right)\right)\Rightarrow−\mathrm{1}\leqslant{ln}\left({log}\left({x}\right)\right)\leqslant\mathrm{1} \\ $$$$\Rightarrow{e}^{−\mathrm{1}} \leqslant{log}\left({x}\right)\leqslant{e}^{\mathrm{1}} \Rightarrow\mathrm{10}^{{e}^{−\mathrm{1}} } \leqslant{x}\leqslant\mathrm{10}^{{e}^{\mathrm{1}} } \Rightarrow \\ $$$${log}\left({ab}\right)={log}\left(\mathrm{10}^{{e}^{−\mathrm{1}} } ×\mathrm{10}^{{e}^{\mathrm{1}} } \right)={e}^{\mathrm{1}} +{e}^{−\mathrm{1}} \Rightarrow\mathrm{2} \\ $$