Chuyen de mu va logarit

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Giáo viên: Nguyễn Tấn Lượng – Ngô Thị Minh Sương.

BÀI TẬP MŨ , LÔGARIT

Giải các phương trình:

1/ 4x + 3. 2x – 10 = 0 2/ 3x-1 + 3x + 3x+1 = 9477 3/ 51+x2

−51− x2=24 4/ 9x

2+1

−3x2+1−6=0
5/ 2√x−21−√x

=1 6/ lg2 lgx −x1=−lgx+lgx −2 1 7/ 4log9x−6 .2log9x

+2log327

8/ 4log3x−5 .2log 3x

+2log39

=0 9/ 9x

−1

−36. 3x2−3+3=0 10/

(

√

)

x+

(

√

)

x −10+3=0
11/ 4x+√x2

−2−5 .2x−1+√x2

−2

=6 12/ 2. 4−
1

x−6−

x

=3 . 9−
1

x 13/ 5x. 8x −x1

=500 14/ 49
1

x−35

x

=25
1

x

15/ x2+1¿x

¿ 16/ ln(x+3) + ln(x-1) = ln(x

2 + 2x -3) 17/ 2log

3(x-2) + log3(x-4)2 = 0

18/ 3lgx = 54 – xlg3 19/ log

3 x.log4 x.log5 x = log3 x.log4 x + log4 x.log5 x + log5 x.log3 x

20/ log3x+7 (9 +12x +4x2) = 4 – log2x+3 (6x2 +23x +21) 21/ |x −1|lg

x −lgx2

=|x −1|3
22/ 252x − x2

+1
+92x− x

=34 .152x −x

23/ (x+ 1)lg(x+1) = 100(x+1) 24/ (x2 – x + 1)x+2 = 1

25/

1− x¿2
¿

logx¿
x¿

26/ xlgx3+5

=105+lgx 27/ log2 (x2 + 2x +3) – log5 (4+ 2 |x| -x2 ) = 0

28/ log3 (x2 + 2x +1) – log3 x = 2x – x2 29/ log2(9−2
x

)

3− x =1 30/

23x− 8

23x−6 .(2
x

− 1

2x−1)=1

31/ logx (2x2 - 7x +12) = 2 32/ log2 (9 – 2x ) = 3 – x 33/ log2x-3 16 = 2 34/ log2x + log4x = log1/2

√

35/ logx 2 – log4 x +7/6 = 0 36/ 5 logx

x+logx
9

x3+8 log9x2x

=2 37/ 22 log3(x
2

−16)
+2log3(x

−16)+1
=24
38/ 1

3log2(5− x)+2 log8

√

3− x=1 39/ lg 5 + lg 10 = 1-lg(2x-1) + lg(21x-20)
40/ 1+2 log4(10− x)= 2

log4x 41/ log4 (log2 x) + log2 (log4 x) = 2 42/ log x+1 (2x3 + 2x2 - 3x +1) = 3

43/ log2 x. log3x = log2 x2 + log3 x3 - 6 44/ 3 .

√

log3x −log33x −1=0 45/ 5|4x−6|=253x−4
46/

(

√

7+4

√

)

cosx+(

√

7−4

√

)

cosx=4 47/ 2x2+4

=22(x

+1)
+

√

22(x

+2)

−2x23+1 48/ log2 x + logx 2= 5/2

49/ log 2x 64 + logx2 16 = 3 50/ log2 (4.3x – 6) – log2 (9x – 6) = 1 51/ 21+log2

x+224

=x2 log2x

52/ log3x+7 (9 + 12x + 4x2) + log2x+3 (21 + 23x + 6x2) = 4 53/ (log2 x)2 + (x-1)log2 x + 2x -6 =0

54/ 3+

1
log32x

=logx
2

(

75x

4 −

x

)

55/

1−2x2¿4

log2¿

log(1−2x2

)x=

4log❑(1−2x2

)(1−2x

2
)−3

Giải các bất phương trình sau:

1/ 52x-1 > 5x + 4 2/

(

√

2+1

)

6x −6

x+1

≤

(

√

2−1

)

− x 3/ 3√x

−2x≥

(

)

x −|x −1|

4/ 51+x – 51-x > 24

5/ 49x - 6.7x – 7 < 0 6/ 6.5x + 1

- 5x + 2 + 6.5x > 22 7/ 2x

2−3x−4

<3x2−3x −4 8/ 5x – 3x+1 > 2(5x-1
-3x-2 )

9/ 7x – 2x+2 5.7x-1 – 2x-1 10/ 2x+3 - 5x < 7. 2x-2 - 3.5x-1 11/ 3x+2 + 7x 4.7x+1 + 34.3x-1

12/ 7x – 5x+2 < 2.7x-1 – upload.123doc.net.5x-1 13/ 4x-1 – 2x-2 < 3 14/ 2x+2 - 2x -3 - 2x+4

> 5x+1 - 5x+2

15/ 22x+1−21 .

(

1
2

)

2x+3

+2≥0 16/ 34−3x−35 .

(

)

2−3x

+6≥0 17/ log3(log1
4

x −log2x+2)<1
18/ ( 4x2- 16x +7 ) log

2(x-3) > 0 19/ log5 [( 2x -4)(x2 – 2x -3) + 1] > 0 20/ xlog2x<32

21/

√

2(5x+24)−

√

5x−7≥

√

5x+7 22/ 5. 36x – 2.81x – 3.16x 0 23/ 8lgx – 19.2lgx – 6.4lgx + 24 > 0
24/ xlg1x

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28/ 3. log8 (x-2) – 6.log8 (x-1) > -2 29/ log2 (x+1) – logx+1 64 < 1 30/ log2
x

x −1≤ −1

31/ log1
2

3x+1

x+1 ≥−1 32/ log14

x −3

x+3≥−

2 33/

log1
2

(1+x −

√

x2−4)≤0

34/ log3(

√

x2−9− x+1

3)≤ −1 35/ log15

(

√

x2−2− x+1)≤0 36/ log

2(2− x −

√

x
2

−1)≥1
37/ log1

2
(x −1

2)+log1
2

(x −1)≤1 38/ log1
2

(x+1

2)+log1
2

x ≥1 39/ log1

√

x+6≤log1

(x+4)

40/ 12log1
5

(x+8)≥log1
5

(x −4) 41/ logx 3

8−2x>−2 42/

log3(x2−7x+12)<

1
log320
¿

43/ log3

√

x
2

−5x+6+log1
3

√

x −2>1

2log1
3

(x+3) 44/ log3

[

log1

(

x2

2 +2

log2x −1

)

]

≤0

45/ lg(x

−3x+2)

lgx+lg 2 >2 46/

x+1¿3
¿
x+1¿2−log3¿

log2¿
¿

47/ log1 1
2

(2x −1)+

1
log2

√

x2−3x

+2 >0

Giải các hệ phương trình sau:

1/

3x. 2y

y − x=2
¿{

2/

2y

=200 . 5x
x+y=1

¿{
¿

3/

x+y¿
1

x − y

(x+y).2y− x=48
¿

1
2

√

3=¿

4/

|x|y=9

234¿
1

y

=2x2
¿
¿
¿{

5/

logx(3x+2y)=2

logy(2x+3y)=2
¿{

6/

logyx −log2y2

log4x −log4y=1

¿{

7/

1
3¿

x−2y

log2(x+y)+log2(x − y)=4
¿

√

3¿x− y=¿
¿
¿

8/

lg2x=lg2y+lg2(xy)

lg2

(x − y)+lgx. lgy=0

¿{

9/

2x.3y=12

2y. 3x=18
¿{

10/

log1+x(1−2y+y2)+log1− y(1+2x+x2)=4

log1+x(1+2y)+log1− y(1+2x)=2
¿{

11/

23x+1

+2y−2=3 .2y+3x

√

3x2

+1+xy=

√

x+1
¿{

12/

logxy(x − y)=1

logxy(x+y)=0
¿{

13/

¿
y2=4x+8

2x+1

+y+1=0
¿{

14/

¿
y2−4x

2x+2+2y+1=0
¿{

15/

y
1
2

=x−1

xy¿x.x− y=y
28x −7y

2
¿
¿
¿{

16/

log4x+log4y=1+log49
x+y −20=0

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17/

logxy+logyx=2

x2− y
=20
¿{

18/

3−x.2y

=1125

log√5(x+y)=2
¿{

19/

log2(x
2

+y2)=5

2 log4x+log2y=4

¿{

20/

3x2

+y2

=81

log2x+log4y=1
¿{

21/

3lgx=4lgy

3y¿lg 3
¿
¿{

4x¿lg 4=¿
¿

22/

log2xy=5

log1
2

x
y=1
¿{

23/

¿
x√y+x=y

4
3

yx+√y

=x
4
3
¿{

24/

9x.3y=81
x+y¿2−lgx=2 lg3

¿
¿
¿{

lg¿

25/

√

y+lgx2=2
y+4 lgx=28

¿{
¿

26/

log2xy . log2x

y=−3

log22x+log22y=5
¿{

27/

¿
x2

=1+6 log4y
y2=2x.y+22x+1

¿{
¿

28/

22x− y+2x=21+y

log2x.(log4y −1)=4

¿{

29/

¿
x2+y2=2

log2(x+y)−log3(x − y)=1
¿{

30/

log5x+log57 . log7y=1+log52

3+log2y=log25(1+3 log5x)
¿{

Giải các bất phương trình sau:

1/ 52x-1 > 5x + 4 2/

(

√

2+1

)

6x −6

x+1

≤

(

√

2−1

)

− x 3/ 3√x

−2x≥

(

)

x −|x −1|

4/ 51+x – 51-x > 24

5/ 49x - 6.7x – 7 < 0 6/ 6.5x + 1

- 5x + 2 + 6.5x > 22 7/ 2x

−3x−4
<3x

−3x −4 8/ 5x – 3x+1 > 2(5x-1

-3x-2 )

> 5x+1 - 5x+2

15/ 22x+1−21 .

(

1
2

)

2x+3

+2≥0 16/ 34−3x−35 .

(

)

2−3x

+6≥0 17/ log3(log1
4

x −log2x+2)<1
18/ ( 4x2- 16x +7 ) log

2(x-3) > 0 19/ log5 [( 2x -4)(x2 – 2x -3) + 1] > 0 20/ xlog2x<32

21/

√

2(5x+24)−

√

5x−7≥

√

5x+7 22/ 5. 36x – 2.81x – 3.16x 0 23/ 8lgx – 19.2lgx – 6.4lgx + 24 > 0

24/ xlg1x

>10x4 25/ log5 (26- 3x ) > 2 26/ log3 (13- 4x ) > 2 27/ log2 (x2 -1) 0

28/ 3. log8 (x-2) – 6.log8 (x-1) > -2 29/ log2 (x+1) – logx+1 64 < 1 30/ log2
x

x −1≤ −1

31/ log1
2

3x+1

x+1 ≥−1 32/ log14

x −3

x+3≥−

2 33/

log1
2

(1+x −

√

x2−4)≤0

34/ log3(

√

x2−9− x+1

3)≤ −1 35/ log15

(

√

x2−2− x+1)≤0 36/ log

2(2− x −

√

x
2−1

)≥1
37/ log1

2
(x −1

2)+log1
2

(x −1)≤1 38/ log1
2

(x+1

2)+log1
2

x ≥1 39/ log1

√

x+6≤log1
3

(x+4)

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1/ 52x-1 > 5x + 4 2/

(

√

2+1

)

6x −6

x+1

≤

(

√

2−1

)

− x 3/ 3√x

−2x≥

(

)

x −|x −1|

4/ 51+x – 51-x > 24

5/ 49x - 6.7x – 7 < 0 6/ 6.5x + 1

- 5x + 2 + 6.5x > 22 7/ 2x

2−3x−4

<3x2−3x −4 8/ 5x – 3x+1 > 2(5x-1
-3x-2 )

> 5x+1 - 5x+2

15/ 22x+1−21 .

(

1
2

)

2x+3

+2≥0 16/ 34−3x−35 .

(

)

2−3x

+6≥0 17/ log3(log1
4

x −log2x+2)<1
18/ ( 4x2- 16x +7 ) log

2(x-3) > 0 19/ log5 [( 2x -4)(x2 – 2x -3) + 1] > 0 20/ xlog2x<32

21/

√

2(5x+24)−

√

5x−7≥

√

5x+7 22/ 5. 36x – 2.81x – 3.16x 0 23/ 8lgx – 19.2lgx – 6.4lgx + 24 > 0

24/ xlg1x

>10x4 25/ log5 (26- 3x ) > 2 26/ log3 (13- 4x ) > 2 27/ log2 (x2 -1) 0

28/ 3. log8 (x-2) – 6.log8 (x-1) > -2 29/ log2 (x+1) – logx+1 64 < 1 30/ log2
x

x −1≤ −1

31/ log1
2

3x+1

x+1 ≥−1 32/ log14

x −3

x+3≥−

2 33/

log1
2

(1+x −

√

x2−4)≤0

34/ log3(

√

x2−9− x+1

3)≤ −1 35/ log15

(

√

x2−2− x+1)≤0 36/ log

2(2− x −

√

x
2

−1)≥1
37/ log1

2
(x −1

2)+log1
2

(x −1)≤1 38/ log1
2

(x+1

2)+log1
2

x ≥1 39/ log1

√

x+6≤log1
3

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Chuyen de mu va logarit

<b>BÀI TẬP MŨ , LÔGARIT</b>

<b>Giải các phương trình:</b>

(

√

)

(

<sub>√</sub>

)

√

√

√

(

<sub>√</sub>

<sub>√</sub>

)

√

<sub>√</sub>

)

√

(

)

<b>Giải các bất phương trình sau: </b>

(

√

)

(

√

)

(

)

(

)

(

)

<sub>√</sub>

√

√

√

√

√

√

√

√

√

[

(

)

]

<sub>√</sub>

<b>Giải các hệ phương trình sau:</b>

<b> 1/ </b>

√

√

√

√

√

<b>Giải các bất phương trình sau: </b>

(

√

)

(

√

)

(

)

(

)

(

)

<sub>√</sub>

√

√

√

√

√

√

√

(

√