一道高一数学题对数log2,详见补充已知log2[log1/2(log2^x)]=log3[log1/3(log3^y)]=log5[log1/5(log5^z)]=0,试比较x,y,z的大小?

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一道高一数学题对数log2,详见补充已知log2[log1/2(log2^x)]=log3[log1/3(log3^y)]=log5[log1/5(log5^z)]=0,试比较x,y,z的大小?
一道高一数学题对数log2,详见补充
已知log2[log1/2(log2^x)]=log3[log1/3(log3^y)]=log5[log1/5(log5^z)]=0,试比较x,y,z的大小?

一道高一数学题对数log2,详见补充已知log2[log1/2(log2^x)]=log3[log1/3(log3^y)]=log5[log1/5(log5^z)]=0,试比较x,y,z的大小?
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