Let x > 1, Y > 1, and 2 (lgY / lgx) - 2 (lgx / lgY) + 3 = 0, find the minimum value of T = x * x-4y * y

Let x > 1, Y > 1, and 2 (lgY / lgx) - 2 (lgx / lgY) + 3 = 0, find the minimum value of T = x * x-4y * y

Equation 2 (lgY / lgx) - 2 (lgx / lgY) + 3 = 0 can be reduced to: 2 (lgY) &# 178; + 3 (lgY) (lgx) - 2 (lgx) &# 178; = 0, i.e. (2lgy lgx) (lgY + 2lgx) = 0 (1) because x > 1, Y > 1, then lgx > 0 and lgY > 0, so lgY + 2lgx > 0, then the solution (1) is: 2lgy lgx = 0, i.e. LG (Y & # 178;) = lgx, so y & # 178; =

Tell me the answer before 12 o'clock this evening, thank you, LG (x + y) + LG (2x + 3Y) - Lg3 = LG4 + lgx + lgY, find the value of X: y

lg(x+y)+lg(2x+3y)-lg3=lg4+lgx+lgyx>=0,y>=0(x+y)(2x+3y)/3=4xy(x+y)(2x+3y)=12xy2x²+5xy+3y²-12xy=02x²-7xy+3y²=0(2x-y)(x-3y)=01.2x-y=02x=yx:y=1:22.x-3y=0x=3yx:y=3:1

If f (2x + 1) = lgx, then f (21)=______ ．

According to the meaning of the question, let 2x + 1 = t (t ＞ 1), then x = 2T − 1, that is, f (x) = lg2x − 1 (x ＞ 1); {f (21) = lg221 − 1 = - 1

If f (x5) = lgx, then f (2)=______ ．

Let t = X5, then x = & nbsp; T15 ｜ f (T) = lgt15 = 15lgt ｜ f (2) = 15lg2, so the answer is 15lg2