如果2^x=5^y=10^z,试以x及y表示z.请付过程?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/26 04:34:54

2^x = 10^z
lg 2^x = lg 10^z
xlg2 = zlg10 z = x lg2
5^y = 10^z
lg5^y = lg10^z
y lg5 = z lg10 z= y lg5
再问：为什么z=xy/(x+y) ???怎么计算出来?
再答：上述式子： z = x lg2 z/x = 1g2 (1) z = y lg5 z/y = 1g5 (2) (1)(2)相加： z/x + z/y = 1g2 + 1g5 z/x + z/y = 1g10 z/x + z/y = 1 z = 1/(1/x + 1/y) = 1/[(x+y)/xy] =xy / (x+y)

如果实数x,y,z满足x^2+y^2+z^2-(xy+yz+zx)=8,用A表示|x-y|,|y-z|,|z-x|中的最试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y) 2x+3y-4z=0.,3x+4y+5z=0,则x+y+z/x-y+z详细的解题过程如果|x+y+z-6|+|2x+3y-z-12|+|2x-y-z|=0求x,y, x/2=y/3=z/5 x+3y-z/x-3y+z 如果,根号x-3+| y-2 |+z^2=2z-1 求（x+z)^y (x+y-z)(x-y+z)= 三元方程求救要过程2x+3y+z=383x+4y+2z=564x+5y+z=66x:y=5:3x:z=7:32x-y-z (4x-2y-z)-{5x[8y-2y-(x+y)]-x+(3y-10z)]=? kuai 3x+2y+z=14 ,x+y+z=10,z+2x+3y=1 5 {5X+Y+Z①X+5Y+Z=-2②X+Y+5Z=10③ {2x+3y-4z=-5 x+y+z=6 x-y+3z=10