Question

高一数学求答案

2.若log2［log1/2（log2x）］=log3［log1/3（log3y］=log5［log1/5（log5z）］=0，则x，y，z的关系是（ ）
A.z＜x＜y B.x＜y＜z C.y＜z＜x D.z＜y＜x

Answer 1

log2[log1/2(log2x)]=log3[log1/3（log3y）]=比log5[log1/5(log5z)]=o,较x,y,z大小

log2[log1/2(log2x)]=0=log2(1)
log1/2(log2x)=1=log1/2(1/2)
log2(x)=1/2
x=2^(1/2)

log3[log1/3（log3y）]=0
log1/3（log3y）=1
log3(y)=1/3
y=3^(1/3)

x^6=2^3=8
y^6=3^2=9
所以y>x

log5[log1/5(log5z)]=o
log1/5(log5z)=1
log5(z)=1/5
z=5^(1/5)
x^10=2^5=32
z^10=5^2=25
所以x>z

所以y>x>z