Question Number 167243 by greogoury55 last updated on 10/Mar/22
$$\:\:\:\:\:\:\mathrm{log}\:_{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{2}\right)<\:\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{3}}{\mathrm{2}}\mid{x}\mid−\mathrm{1}\right)\: \\ $$
Answered by MJS_new last updated on 10/Mar/22
$$\mathrm{lhs}=\mathrm{rhs}\:\Rightarrow\:{x}=\pm\mathrm{2};\:\mathrm{lhs}\:\mathrm{defined}\:\mathrm{for}\:\mid{x}\mid>\sqrt{\mathrm{2}} \\ $$$$\Rightarrow \\ $$$$−\mathrm{2}<{x}<−\sqrt{\mathrm{2}}\vee\sqrt{\mathrm{2}}<{x}<\mathrm{2}\:\mathrm{same}\:\mathrm{as}\:\sqrt{\mathrm{2}}<\mid{x}\mid<\mathrm{2} \\ $$
Commented by greogoury55 last updated on 12/Mar/22
$${yes}.\:{thank}\:{you} \\ $$