log^x(x-2)*log^x(x+2)>0 desigualdades

Se da la desigualdad:
$$\log{\left(x - 2 \right)}^{x} \log{\left(x + 2 \right)}^{x} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\log{\left(x - 2 \right)}^{x} \log{\left(x + 2 \right)}^{x} = 0$$
Resolvemos:
$$x_{1} = -105.118875071184 + 1.38646561737862 i$$
$$x_{2} = -19.5199290889381 + 2.31572761056288 i$$
$$x_{3} = -87.1644763425275 + 1.45832315877969 i$$
$$x_{4} = -25.4608396921231 + 2.1126228622645 i$$
$$x_{5} = -85.1701319850533 + 1.46759145157227 i$$
$$x_{6} = -73.2071880583622 + 1.5304532950715 i$$
$$x_{7} = -15.5681609114383 + 2.51587862858424 i$$
$$x_{8} = -35.3840488544782 + 1.89849594655961 i$$
$$x_{9} = -75.200603551132 + 1.51900165132165 i$$
$$x_{10} = -95.1431119565465 + 1.42403878397291 i$$
$$x_{11} = -81.181861381516 + 1.48708072811972 i$$
$$x_{12} = -13.5968524391923 + 2.65031823891268 i$$
$$x_{13} = -27.4436555305889 + 2.06053589621617 i$$
$$x_{14} = -33.3977638274348 + 1.9335114538576 i$$
$$x_{15} = -61.2509140767952 + 1.60989349398239 i$$
$$x_{16} = -55.2760562269411 + 1.65850218787364 i$$
$$x_{17} = -39.3585716423455 + 1.83653239140527 i$$
$$x_{18} = -23.4791646618538 + 2.17135018542683 i$$
$$x_{19} = -59.2590172790959 + 1.62531056284528 i$$
$$x_{20} = -79.1879483623184 + 1.49734063345215 i$$
$$x_{21} = -83.1759248677926 + 1.47717109238214 i$$
$$x_{22} = -41.3466997021974 + 1.80891292936479 i$$
$$x_{23} = -65.2354598407137 + 1.58111426625679 i$$
$$x_{24} = -101.128270622784 + 1.40087039633431 i$$
$$x_{25} = -77.1941931332931 + 1.5079728996923 i$$
$$x_{26} = -53.2850287807189 + 1.67642148574775 i$$
$$x_{27} = -37.3710042670513 + 1.86629228341476 i$$
$$x_{28} = -89.1589519574163 + 1.44934902951227 i$$
$$x_{29} = -93.1482748701186 + 1.43222098184407 i$$
$$x_{30} = -43.3353431915767 + 1.783181288334 i$$
$$x_{31} = -69.2209163999132 + 1.55474406854811 i$$
$$x_{32} = -49.3039862108778 + 1.71534551030227 i$$
$$x_{33} = -63.2430664961919 + 1.59517931382377 i$$
$$x_{34} = -67.2280806150839 + 1.56765024933939 i$$
$$x_{35} = -45.3244619763413 + 1.75912513100995 i$$
$$x_{36} = -97.1380598257392 + 1.41609397763306 i$$
$$x_{37} = -29.4274833006894 + 2.0138956056109 i$$
$$x_{38} = -21.4987908971154 + 2.23831762867003 i$$
$$x_{39} = -17.5428825380106 + 2.40670977713814 i$$
$$x_{40} = -99.1331140928403 + 1.40837482496147 i$$
$$x_{41} = -9.69133984413244 + 3.0441032861565 i$$
$$x_{42} = -31.4122161745812 + 1.97179065963406 i$$
$$x_{43} = -51.2943309868906 + 1.69533602153123 i$$
$$x_{44} = -91.1535532213376 + 1.44065319650701 i$$
$$x_{45} = -11.6322287442974 + 2.82121623594766 i$$
$$x_{46} = -71.2139557420454 + 1.54235680753043 i$$
$$x_{47} = -2$$
$$x_{48} = -103.123525511902 + 1.393570499705 i$$
$$x_{49} = -47.3140203069425 + 1.73656445821022 i$$
$$x_{50} = -57.2673921448841 + 1.64149082188258 i$$
Descartamos las soluciones complejas:
$$x_{1} = -2$$
Las raíces dadas
$$x_{1} = -2$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{1}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$-2.1$$
lo sustituimos en la expresión
$$\log{\left(x - 2 \right)}^{x} \log{\left(x + 2 \right)}^{x} > 0$$
$$\frac{1}{\log{\left(-2.1 - 2 \right)}^{2.1} \log{\left(-2.1 + 2 \right)}^{2.1}} > 0$$

                                               -2.1                              -2.1    
0.0842071065173066*(1 + 0.708723764735013*pi*I)    *(-1 + 0.434294481903252*pi*I)     > 0
    

Entonces
$$x < -2$$
no se cumple
significa que la solución de la desigualdad será con:
$$x > -2$$

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