El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\log{\left(4 \sin{\left(2 x \right)} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{2} + \frac{\pi}{2}$$
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{2}$$
Solución numérica$$x_{1} = -65.8471055978146$$
$$x_{2} = -1.69713645436594$$
$$x_{3} = -23.6882850294945$$
$$x_{4} = -73.9537674869312$$
$$x_{5} = 57.9931239638401$$
$$x_{6} = -21.8648084475575$$
$$x_{7} = -50.1391423298656$$
$$x_{8} = -72.1302909049942$$
$$x_{9} = 79.9842725389687$$
$$x_{10} = 42.2851606958912$$
$$x_{11} = -89.6617307548802$$
$$x_{12} = -95.9449160620597$$
$$x_{13} = -43.8559570226861$$
$$x_{14} = -67.6705821797516$$
$$x_{15} = 94.3741197352648$$
$$x_{16} = -94.1214394801228$$
$$x_{17} = -28.1479937547371$$
$$x_{18} = 86.2674578461483$$
$$x_{19} = 44.1086372778281$$
$$x_{20} = -87.8382541729432$$
$$x_{21} = 88.0909344280852$$
$$x_{22} = -29.9714703366741$$
$$x_{23} = -51.9626189118026$$
$$x_{24} = 66.0997858529567$$
$$x_{25} = 64.2763092710197$$
$$x_{26} = 36.0019753887116$$
$$x_{27} = -7.98032176154552$$
$$x_{28} = 22.1174887026996$$
$$x_{29} = 14.010826813583$$
$$x_{30} = -45.679433604623$$
$$x_{31} = 20.2940121207626$$