已知lgx-lgy=a,则lg(2分之x)3 -Lg(2分之y)3
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2/3lgx-3(lgy-lg100)=2/3*a-3(b-2)
lgx+lgy=lgxy=a原式=lg[x^n*x^(n-1)*……*x*y^n*……*y]=lg{(xy)^[1+2+……+n]}=(1+2+……+n)*lgxy=an(n+1)/2
lgx^2+lgy=42lgx+lgy=4≥2Sqrt[2lgx×lgy]Sqrt[2lgx×lgy]≤22lgx×lgy≤4lgx×lgy≤2
lg(x2)3−lg(y2)3=3(lgx-lg2)-3(lgy-lg2)=3(lgx-lgy)=3a故选A.
2lg(x-2y)=lgx+lgylg(x-2y)²=lgxy(x-2y)²=xyx²-5xy+4y²=0用x表示y解得两根为x=4y或x=yy/x=1/4或y
lg(x-2y)=1/2(lgx+lgy)lgxy=2lg(x-2y)=lg(x-2y)^2(x-2y)^2=xyx^2-4xy+4y^2=xyx^2-5xy+4y^2=0(x-4y)(x-y)=0x
lg(x-y)+lg(x+y)=lg2+lgx+lgy左边=lg[(x-y)(x+y)]=lg[x^2-y^2]右边=lg(2xy)左边=右边所以lg[x^2-y^2]=lg(2xy)x^2-y^2=
lg(x+y)+lg(2x+3y)=lg12+lgx+lgylg[(x+y)(2x+3y)]=lg(12xy)(x+y)(2x+3y)=12xy2x^2+5xy+3y^2=12xy=02x^2-7xy
(X-2Y)^2=XYX^2-5XY+4Y^2=0(X-Y)(X-4Y)=0X=Y(不合题意舍去)或X=4Y∴X/Y=4再问:为什么舍去啊再答:由lgX与lgY知X>0,Y>0X-2Y=-X
∵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,当且仅当3xy=8yx,x+2y
由对数性质及题干lg(x+y)=lgx+lgy=lgxy即x+y=xy,(x,y>0)亦即(1/y)+(1/x)=1故(4x+y)=(4x+y)*1=[(1/y)+(1/x)](4x+y)=(4x/y
2lg(x-2y)=lgx+lgy则lg(x-2y)^2=lg(xy)(x-2y)^2=xyx^2-5xy+4y^2=0x-2y大于0则x大于2yx大于0y大于0(x-y)(x-4y)=0x1=y舍去
1、解对数方程:(x-2y)^2=xyx^2-5xy+y^2=0得x=4y或x=y所以,x/y=4或12、不等式两边用同底对数表示:lg(10^a)1,则f(x)的图像在(-1,0)上是负数,不合题目
∵2lg(x-2y)=lgx+lgy,∴lg(x-2y)2=lgxy,∴(x-2y)2=xy,∴x2-5xy+4y2=0,∴(xy)2-5•xy+4=0,∴xy=1(舍去),或xy=4,故答案为4.
∵2lg(x-2y)=lgx+lgy,∴x−2y>0x>0,y>0(x−2y)2=xy,解得xy=4.∴log2xy=log24=2.故答案为2.
lg((x-y)/2)^2=lg(xy),化简后得x2-2xy+y2=4xy,同除以4x2得,1/4+y/2x+y2/4x2=y/x令y/x=a,解得a=土2倍根号2+3,1/a=他的倒数,f(0)=
lg根号x-lg(y/10)^2=lgx^(1/2)-2lg(y/10)=1/2*lgx-(2lgy-2)=(a/2)-2b+2
lg√x=1/2lgxlg(y/10)∧2=2lg(y/10)=2(lgv-1)lg√x-lg(y/10)∧2=1/2a-2b+2
x>0y>0x-2y>0lgx+lgy=2lg(x-2y)lgxy=lg(x-2y)²xy=(x-2y)²x²-5xy+4y²=0x=y(舍)或x=4yx/y=