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Решите задачу:

${lg}^{2} (100x) + {lg}^{2} (10x) + {lg}^{2} x = 14 \\ {lg}^{2} 100 + {lg}^{2} x + {lg}^{2} 10 + {lg}^{2} x + {lg}^{2} x = 14 \\ 4 + {lg}^{2} x + 1 + {lg}^{2} x + {lg}^{2} x = 14 \\ 3 {lg}^{2} x + 5 = 14 \\ 3 {lg}^{2} x = 9 \\ {lg}^{2} x = 3 \\1) \: \: lgx = 3 \\ x = {10}^{3} = 1000 \\ 2) \: \: lgx = - 3 \\ x = {10}^{ - 3} = 0.001$