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?
问题描述：
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?
答
log2[log1/2(log2x)]=0=log2(1)log1/2(log2x)=1=log1/2(1/2)log2(x)=1/2x=2^(1/2)log3[log1/3（log3y）]=0log1/3（log3y）=1log3(y)=1/3y=3^(1/3)x^6=2^3=8y^6=3^2=9所以y>xlog5[log1/5(log5z)]=olog1/5(log5z)=1log...