lg ^ 2 200 * log2 10 - ( lg 2 - 2 ) ^ 2 / lg 2 = lg ^ 2 200 * 1 / lg 2 - ( lg 2 - 2 ) ^ 2 / lg 2 = lg ^ 2 ( 100 * 2 ) * 1 / lg 2 - ( lg 2 - 2 ) ^ 2 / lg 2 = ( lg (100 * 2 ) ) ^ 2 * 1 / lg 2 - ( lg 2 - 2 ) ^ 2 / lg 2 = ( lg (100 * 2 ) ) ^ 2 / lg 2 - ( lg 2 - 2 ) ^ 2 / lg 2 = ( ( lg (100 * 2 ) ) ^ 2 - ( lg 2 - 2 ) ^ 2 ) / lg 2 = ( ( lg 100 + lg 2 ) ) ^ 2 - ( lg 2 - 2 ) ^ 2 ) / lg 2 = ( ( lg 10 ^ 2 + lg 2 ) ) ^ 2 - ( lg 2 - 2 ) ^ 2 ) / lg 2 = ( ( 2 + lg 2 ) ) ^ 2 - ( lg 2 - 2 ) ^ 2 ) / lg 2 = ( ( 2 + lg 2 ) ) ^ 2 - ( lg 2 - 2 ) ^ 2 ) / lg 2 = ( 2 + lg 2 + lg 2 - 2 ) * (2 + lg 2 - ( lg 2 - 2 ) ) / lg 2 = 2 * lg 2 * (2 + lg 2 - ( lg 2 - 2 ) ) / lg 2 = 2 * (2 + lg 2 - ( lg 2 - 2 ) ) = 2 * (2 + lg 2 - lg 2 + 2 ) = 2 * (2 + + 2 ) = 2 * 4 = 8.