一道高中数学题lg2+lg5=lg10,lg2.lg5=?
2个回答

设 lg2 = x ,则 10^x = 2

lg5 = y ,则 10^y = 5

因为:2×5 = 10

即 10^x × 10^y = 10^(x+y) = 10

10^(x+y) = 10 其实就是 (x + y) = 1

两边取对数 (x+y) = Lg10

所以:lg2 + lg5 = x + y = lg10 = 1

Lg2×Lg5 = x×y = Lg[2^(Lg5)] 或者 Lg[5^(Lg2)]