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Given LG (x + 2Y) = lgx + lgY, the minimum value of 3x + 4Y is______ ．
∵ LG (x + 2Y) = lgx + lgY, ∵ x ＞ 0, y ＞ 0. X + 2Y = XY, ∵ 2x + 1y = 1, ∵ 3x + 4Y = (3x + 4Y) (2x + 1y) = 6 + 4 + 3xy + 8yx ≥ 10 + 26, if and only if 3xy = 8yx, x + 2Y = XY, X ＞ 0, y ＞ 0, take the equal sign. The minimum value of ∵ 3x + 4Y is 10 + 26
Let X and y satisfy lgx + lgY = 2, then the minimum value of X + 4Y is ()
A. 100B. 40C. 4D. 2
∵ lgx + lgY = 2, ∵ X and y are positive numbers, and lgxy = 2. From the relationship between exponent and logarithm, we can get xy = 100, ∵ x + 4Y ≥ 2x · 4Y = 40, if and only if x = 4Y, that is, x = 20 and y = 5, the equal sign holds, and the minimum value of ∵ x + 4Y is 40, so we choose: B
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