1.若2^x=5^y=10^z,xyz不等于0,则.(2^x的意思是2的x次方)A.z=(x-y)/(x+y)B.z=xy/(x+y)C.z=xy/(x-y)D.z=(x+y)/xy3.函数y=x^(-2/5)的单调递减区间为.(y=x^(-2/5)的意思是y=x的(-2/5)次方)

Question

1.若2^x=5^y=10^z,xyz不等于0,则______.(2^x的意思是2的x次方)
A.z=(x-y)/(x+y) B.z=xy/(x+y) C.z=xy/(x-y) D.z=(x+y)/xy
3.函数y=x^(-2/5)的单调递减区间为_______.(y=x^(-2/5)的意思是y=x的(-2/5)次方)

Answer 1

2^x=5^y=10^z
取对数
xlg2=ylg5=zlg10
令xlg2=ylg5=zlg10=k
lg2+lg5=lg10
所以k/x+k/y=k/z
即xz+yz=xy
z=xy/(x+y)
选B
y=x^(-2/5)
在(0,+∞)上单调递减