高一的对数题

(1)
3^a=7^b=√21 1/a+1/b
Log(3)√21=lg√21/lg3=a
1/a=lg3/lg√21
Log(7) √21=lo√21/lg7=b
1/b= lg Log7/ lg√21
1/a+1/b
= lg3/lg√21+ lg Log7/ lg√21
= (lg3+lg Log7)/ lg√21
= lg21/ lg21^(1/2)
=2

(2)
4^a=5^b=m,1/a+2/b=1
a=log(4)m=lgm/lg4=lgm/2lg2
1/a=2lg2/lgm
b=log(5)m=lgm/lg5
1/b=lg5/lgm
1/a+2/b
=2lg2/lgm+2lg5/lgm
=2(lg2+lg5)/lgm
=2lg10/lgm
=2/lgm
=1
lgm=2=lg100
m=100

(3)
lg√45
=1/2lg45
=1/2lg3^2*10/2
=1/2(2lg3+lg10-lg2)
=lg3-1/2lg2+1/2
=0.4771-0.3010/2+0.5
=0.8266

(4)
log(8)9
=2lo3/3lg2
=(2/3)lg3/lg2
=a
lg3=(3/2)(lg2)a---------(1)
log(2)5
=log(2)10/2
=log(2)10-log(2)2
=lo10/lg2-1
=1/lg2-1
=b
lg2=1/(b+1)----------(2)
(2)代入(1)得
lg3=(3/2)(lg2)a
=(3/2)[ 1/(b+1)]a
=3a/2(b+1)

(5)
log(56)7
=lg7/lg56
=lg7/(lg7