請問:(1)設logx的首數2且logx的尾數是log3x尾數的3倍，則x=?(2)設10<x<100，且log(x^2)之尾數為log(1/x)之尾數的3倍，則x=?

(1)設logx的首數2且logx的尾數是log3x尾數的3倍，則x=?
Sol
logx的首數2
logx=2+a，0<=a<1
log(3x)=log3+logx=2+log3+a
log3+a>1
log(3x)=3+(log3+a－1)
a=3(log3+a－1)
a=log27+3a－3
2a=3－log27
log(x^2)=4+2a=7－log27=log(10^7/27)
x^2=10^7/27=3*10^7/81
x=1000√30/9
(2)設10<x<100，且log(x^2)之尾數為log(1/x)之尾數的3倍，則x=?
Sol
10<x<100
100<x^2<10000
log100<log(x^2)<log10000
2<log(x^2)<4
log(x^2)=2.????? or log(x^2)=3.?????
10<x<100
1/100<1/x<1/10
log(1/100)<log(1/x)<log(1/10)
-2<log(1/x)<-1
log(1/x)=-1.?????=－2+0.?????
log(1/x)之尾數=2+log(1/x)
(a) log(x^2)=2.????
log(x^2)-2=3[2+log(1/x)]
2logx-2=6-3logx
5logx=8
logx=8/5
x=10^(8/5)……………………
(b) log(x^2)=3.?????
log(x^2)－3=3[2+log(1/x)]
2logx－3=6-3logx
5logx=9
logx=9/5

x=10^(9/5)
驗算不合