Logarit(1) Bµi I TÝnh:
10
3
3
1
2
2
10 3
1
1) log ;
100
2) log 3
3) log 4
1
4) log
2
1
5) log
10
3
0,5
log 12
log 1
1 5
6)9 7)0,125 8) log 125
0,5
1 4
1 9) log
2 1 10) log
64
3 3 2 2
1 6 log 18
5 log 2 log 5 log 5
11) log 36
12)3 13)3
1 14)( )
8 1 15)
32
Bµi II.TÝnh:
7
4
3
log 16
1)
log 15 log 30
2) log log 4 log 3
1 3) log 3 log 12 log 50
2 1
4) log 36 log 14 3 log 21
2
−
5
5) log 12 log 15 log 20
log 36 log 12
6)
log 9
−
log 5 1 log2 log 3
8)log log36 log
−
1 1 9)lg lg 4 4 lg 2
8 2 1 10)lg lg 0,375 2 lg 0,5625
8
27 11)lg72 2 lg lg 108
256
12) 9 2 log 4 4 log 23 + 81
Bµi III T×m x, biÕt:
( )
3
1) log 1 2
2) log 4 log 7 log
3 3) log log
2
x
4)log 2log 3log 5)log 27 3x
= 1
7
x
x
= −
= −
Bµi IV Kh«ng dïng m¸y tÝnh, h·y so s¸nh:
2)3log2+lg3 vµ 2lg5 4) 1+2lg3 vµ lg27
Bµi V BiÓu diÔn logarit sau qua a vµ b:
1) log 50;3 a = log 15;3 b = log 103 2)log 1250;4 a = log 52
Trang 2Logarit(2) Bµi I TÝnh:
4
3
5
1
3
2 log 4
log 8
log 2 log 3
2)36
3) log 4 log 2 log 2
4)4 8
5)25
6) log 5 log 2 log 7 log 3
+
+
−
3
9
log 5
7)36 + 3 − 3
2 3
3
2 log 2
log 4
8)
27
−
4
1
3 4 1 3
3
15 3 5
27 log 27 log
9 9)
log 2.log 3.log 4.log 5.log 6.log 7 10)
log 6.log 9.log 2 log 135 log 5
11)
−
Bµi II.1) Cho log 2712 =m tÝnh log 616 theo m
2) Cho log23=a; log52=b TÝnh log125 vµ log 10 302 theo a vµ b?
3) Cho log303=a; log305=b; TÝnh log302 theo a vµ b
4)Cho a=log23; b=log35; c = log 27 3 tÝnh log14063?
5) Cho log315=a; log310=b tÝnh log 503 theo a vµ b.
Bµi III Chøng minh:
( )
.
log log 1) log
1 log
+
=
+
a x
a
bx
+
k
k k
3) NÕu a2 +b2 =c a b c2( ; ; >0;c b± ≠1) th× logb c+ a + logc b− a = 2logb c+ a logc b− a
4) NÕu logxa; logyb; logzc t¹o thµnh mét cÊp sè céng th× 2 log log
log
=
+
b
y
5) lg(x+2y)-2lg2=1
2(lgx+lgy) víi x,y > 0; x2 + 4 y2 = 12 xy
6) Cho a=log1218; b=log2454 C/m: ab+5(a-b)=0