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01) )log()log( baba □ )log( 22 ba □
2)log( ba □ 22 loglog ba □ nuk modifikohet
02) ba log2log2 □ ablog4 □ ablog2 □
44log ba □ )log( 22 ba
03) 2
1log4log
2
1
2
1 □ –2 □ 1 □ 3 □ 1
04) xxx log2loglog3 □
3log x □ xlog □ 5log x □
4log x
05) 58 x □ 5log8log x □ 5log
8logx
□ 8
5x
□ 8log
5logx
06) 3log aa
□ 3
2
□ 2
3
□ 3a □ 3
07) 877 1 xx □ 3x □ 2x □ 1x □ 1x
08) 11 5:3 xx
□
2)1(
5
3 x
□
1
5
3 x
□
1
5
3
x
□
1
3
5 x
09) )3log(log xx □ )2log( x □ )3log( x □ 3
1log
□ e pamundur
10) 13:3 xx
□ xx 2
3 □ 13 xx
□ 3 □ x3
11) )3log()2log( xx □ x6log □ )6log( x □
26log x □ e pamundur
12) 11 22 xx
□ 1
1
2 x
x
□ 4 □
x22
3
□
4
1
13) 3)(log)(log yxyx aa □ )(log 22 yxa □ )(log 33 yxa □ )(log2 yxa □ )(log 33 yxa
14)
xx
ba
2
:3
□ a
b
2
3
□
x
a
b
3
2
□
x
a
b
2
3
□
x
ab
6
15) )log(log yx □ e pamundur □ )log( xy □ y
xlog
□
xy
1log
16) 333 352
□
3
3
52
□ 973 □ 3)352( □ 106
17) 2)1(log3 x □ 8x □ 5x □ 1x □ 3x
18) a
b
2 □
b a2 □ b
a
2
1
□ a
b
2
1
□ b
a
2
2
19) 11 28 xx
□ 12 x □
14 x □
110 x □
116 x
20) yx aa □
yxa □
xya □ yx □ nuk modifik
01) yx aa loglog □ )(log yxa □ y
xalog
□ x
yalog
□ xyalog
02) )(log baa □ ba aa loglog □ aa ba loglog □ balog1 □ nuk modifikohet
03) 1log2log 44 □ –2 □ 2
1
□ 2
1
□ 2
04) 33 3log2log
□ 3
2log3
□ 2
3log3
□ 3
2log2
□ 2
3log2
05) a
b
2
□ b a2 □
b
a
2
1
□ a
b
2
1
□ a b2
06) 2log aa □ 1 □
2a □ 0 □ 2
07) yxyx aa 2: □
xa 3 □
yxa □
xa3 □
ya
08) 11 53 xx
□ 2)1(15 x
□ 115 x □
2215 x □
18 x
09) )log(log xx □ )log( 2x □
2)log( x □ 0 □ e pamundur
10) 33 3:2
□
3
3
2
□
3
2
3
□ 9
4
□ 36
11) baba 2:2 □
22
2 ba □
b22 □ b22 □
a22
12) 11 22 xx
□ )1)(1(2 xx □
x22
5
□ 1 □ x22
13) 3)(log)(log yxyx aa □ )(log 22 yxa □ )(log 33 yxa □
4)(log yxa □ )(log 33 yxa
14) )log()log( baba □ )log( 22 ba □ 22 loglog ba □
2)log( ba □ 2)log( ba
15) 11 : xx aa
□ 12 xa □
1
1
x
x
a □ 2a □
2xa
16) 333 352
□
3
3
52
□ 100 □ 3)532( □ 106
17) 1log3log 22 □ 4log 2 □ 3log2 □ 1log2 □ 2log2
18) xx log)1log( □ )12log( x □ )1log( □ x
x 1log
□ 1log
xx
19) )log()log( baba □ a2log □ b2log □ ba
ba
log □ )log(
)log(
ba
ba
20) 3log22log3 32 □ 36log6 □ 5 □ 6 □ 6log6
21)
xx
ba
1
:1
□ a
b
□ b
a
□
x
a
b
□ xab)(
22) )log()log(2 baba □ )log( ba □ )log( 22 ba □ )log( 22 ba □ e pamundur
23) 35 x □ 5log3log x □ 5log
3logx
□ 3log5log x □ 3log
5logx
23) 3)1(log 2 x □ 7x □ 5x □ 1x □ 3x
24) xx log)1log( □ 2
1x
□ 0x □ 1x □ e pamundur
25) yxyx 22
□ 22
2 yx □ y22 □
yx
yx
2 □ )12(
2
2 2 yy
x
26) yx aa
□ yx □ y
x
a □ yxa □ nuk transformohet
27) zyx 101010 □
zyx 10 □ xyz10 □
xyz1000 □ nuk transformohet
28) xx aa 2loglog □ )(log xa □ xalog □ 2
1log a
□ nuk transformohet
29) 11 22 xx
□ )1)(1(2 xx □
22 □
x22
5
□ x22
30) 11 2:8 xx
□ 12 x □
14 x □
16 x □
04
31) 1log2log 88 □ 3 □ 3
1
□ 3
1
□ 3
32) 11 : xx aa
□ a □ xa 2 □
2
1
a □ 2a
33) 5log225log □ 0 □ 1 □ 5log □ 10log
34) )log()log( yx □ e pamundur □ xylog □ y
xlog
□ xy
1log
35) ba log2log3 □ )23log( ba □ ab6log □
ba23log □ 23log ba
36) ba log
2
1log
3
1
□ b
a3
log □ 6
logab
□ 6logb
a
□ )log(3 ba
37) xx loglog2 3 □ 4log2 x □
7log x □ 10log x □
5log x
38) 22 loglog ba
□
2
log
b
a
□
2
log
a
b
□ )(log baba □ )log(log baba
39) xx 222 □ )21(2 xx □
32 □ 222 x □ nuk transformohet
40) yx 22 □
xy2 □ yx2 □ )(2 yx □ nuk transformohet
41) 1 13 x x
□ 1
1
3 x
x
□ 1
1
3 x
x
□ 1
1
3
3
x
x
□ 1
1
3
3
x
x
42) 1loglog x □ e pamundur □ xlog □ 0 □ )1log( x
43) yx 3log3log □
yx3log □ 7log x □
10log x □ yx 33log
44) )4log()3log( □ e pamundur □ 12log □ 12
1log
□ )7log(
45) xx
1loglog
□ e pamundur □ 0 □
xx
1log
□ )1log( x
46) a
b
2 □
b a2 □ b
a
2
1
□ a
b
2
1
□ b
a
2
2
47) 2024 xx □ 3x □ 2x □ 1x □ 1x
48) )log()log( baba □ )(21 baog □ )log( 22 ba □ a2log □ ba
ba
log
49) xx 3log5log □ 1251ogx □ 81ogx □
15log x □ x15log
50) 3
1
3
1
2:3 □
3)5.1( □ 3 6.0 □
3 5.1 □ 2
3
1) 3 7 3 3 71x x x x xٱ xٱ 3 xٱ 0 ٱ 1 x 1
2) 3 9 4 3 7 0 x xxٱ xٱ 3 xٱ 2 ٱ 0 x 1
3) log( ) log( ) logx x x 2 2 3 2 xٱ xٱ 5 xٱ 6 ٱ 2 x 4
4) 3 5 202 1x x ٱ
xgol001
ٱ 54x
gol
gol
001
xٱ 57 gol gol001 ٱ 54
x log
log
100
45
5) 8 4 163 5x x x xٱ xٱ 3 xٱ 2 ٱ 4 x 1
zgjidhni:
1) 4 2 20x x xٱ xٱ 3 xٱ 2 ٱ 1 x 1
2) 3 3 3 5 2 5 2 52 1 2 1x x x x x x
xٱ xٱ 3 xٱ 2 ٱ 0 x 1
3) log( ) log( ) log2 1 2 x x
xٱ x 3 2; xٱ x 0 1; xٱ x 1 1; ٱ x x 1 2;
4) 3 2 83 1x x
ٱ x
gol
gol
42
ٱ 4x
gol
gol
4
ٱ 42x
gol
gol
1
ٱ 6 x
log
log
6
18
5) 2 8135
3x x ٱ
x 3
ٱ x 2
ٱ x 1
ٱ x 1 ekuacione logaritmike:
a) log( ) log( ) logx x 1 3 4 b) log( ) log( ) log log( )x x x x 2 1 1
c) log( ) log log( ) logx x 1 3 1 5
ekuacione eksponenciale:
1. a) 2 8 41 23x x b) 3 27 91 1x x x c) 3 27 91 1x x
2. a) 2 3 2 20 01x x b) 2 4 6 0x x c) 2 2 121 1x x
3. a) 5 7 101x x b) 3 5 71 2x x x c) 7 4
5
61
1x
x
4. a) 3 3 51x x x b) 5 7 5 72 1x x x x
5 2 5 21 1 2 1x x x x 5. Zgjidhni:
6. a) log 1
9
9 x b) log2 2 x c) log x 125 3 d)
log x1
42
e) log9
1
2x
f) log 1
3
3x
7. Cila eshte zgjidhja e ekuacionit: 3 3 32 3x x
x = 1 x =
2
3 x = 1; x = 1 x =
3
2
8. Percaktoni zgjidhjen 5 26 5 25 02 x x
x = 0; x = 2 x = 25; x = 1 x = 1; x = 2 x =
3
2 ; x = 0.
3. gjeni zgjidhjen: log( ) log log( )2 1 2 3x x
x =
5
4 x =
4
5 x = 4 asnjera
4gjeni zgjidhjen: 2 2 1 5 8log( ) log( ) log( )x x x
7) zgjidhni ekuacionin eksponencial: 4 2 12x x ٱ ٱ 1ٱ 2ٱ 2 3
8) Zgjidhni ekuacionin eksponencial: 3 3 272 1x x ٱ 1ٱ -1ٱ 2ٱ 2
9) Zgjidhni ekuacionin eksponencial 5 2 71x x
golٱ gol41 01 ٱgol
gol
7
ٱ 5gol
gol
41
ٱ 01
log
log
10
14
10) zgjidhni ekuacionin eksponencial 3 5 5 31 2x x x x
ٱ
gol
gol
215
ٱ 3
gol
gol
213
ٱ 5
gol
gol
3
5ٱ 21
log
log( )
12
3 5
B1) zgjidhni ekuacionin logaritmik: 3log52log)12log(log xxx
B2) xxxx 1log1log)13log(14log
B3. Zgjidhni ekuacionin eksponencial: xx 369
Zgjidhni:
01) xxx log232log2log
02) xLogxLogxLog 321325
03) 12 365252034 xxxx
04) 26552 xx
05) 53 1648 xxx
06) 4023 213 xx
01) 3
82332 xx
02) 825 321 xx
03) 12 365252034 xxxx
04) xxx log232log2log
05) 52 9273 xxx
Logaritmet dhe eksponentet
01) abba xx 2:
[]ax
[]abx 3
[]bax 3
[]ax3
02) 2loglog aa
[] e pamundur []3log a [] a
1log
[] alog
03) 2024 xx [] 3x [] 2x [] 1x [] 1x
04) 073493 xx [] 3x [] 2x [] 0x [] 1x
05) x27log
3 [] 5x [] 2
3x
[] 6x [] 3x
06) 3
53 1 82
x
x [] 3x [] 2x [] 1x [] 1x
07) 53 1648 xxx [] 3x [] 2x [] 4x [] 1x
08) 32log x []
6
2
1x
[]6 2x [] 2x [] 6
1x
09) 4
1
4
1log x
[] 128
1x
[] 256x [] 256
1x
[]8
2
1x
10) 3
1
2
1
4
3
xxx []19 12x []
12 7xx []xlog
12
19
[]x
12
19log
11)
2)1(log2
1 x
[] 3x [] 1x [] e pamundur [] 3
1x
12) 7 01,0log
[]10log
7
2
[]10log
2
7
[]10log
7
2
[]10log
2
7
13) 43 logloglog cba []
cba log4
1log
3
1log
2
1
[] 3
4
logb
ca
[]cba log
4
1log
3
1log
2
1
[]4
3
logc
ba
14) x8log3 2
[] 2
9x
[] 8
1x
[] 16
1x
[] 16x
15) 2
1log
2
1 x [] 2
1x
[] 2
1x
[] 2
1x
[] 2x
16)
2log4
1 x
[] 8x [] 8
1x
[] 16x [] 2
1x
[] 2log aa □ 1 □
2a □ 0 □ 2
[] yxyx aa 2: □
xa 3 □
yxa □
xa3 □
ya
[] 11 53 xx
□ 2)1(15 x
□ 115 x □
2215 x □
18 x
[] )log(log xx □ )log( 2x □
2)log( x □ 0 □ e pamundur
[] 33 3:2
□
3
3
2
□
3
2
3
□ 9
4
□ 36
[] baba 2:2 □
22
2 ba □
b22 □ b22 □
a22
[] 11 22 xx
□ )1)(1(2 xx □
x22
5
□ 1 □ x22
[] 3)(log)(log yxyx aa □ )(log 22 yxa □ )(log 33 yxa □
4)(log yxa □ )(log 33 yxa
[] )log()log( baba □ )log( 22 ba □ 22 loglog ba □
2)log( ba □ 2)log( ba
[]11 : xx aa
□ 12 xa □
1
1
x
x
a □ 2a □
2xa
[] 333 352
□
3
3
52
□ 100 □ 3)532( □ 106
[] 1log3log 22 □ 4log 2 □ 3log2 □ 1log2 □ 2log2
[]
5
3
3 2
162
2
x
x
[]
5 1
3 12
2
32
x
x []
xx
x
279
31
3 2
[]xx
x
125
1
5
251
1
[] 6522 33 xx [] 922 12 xx
[] 2022 31 xx [] 322 32 xx
[]x
xx
7
425 21
[]
xx
x
57
33
1
[] 2311 3553 xxxx []
2211 2552 xxxx
[] 2log)5(log 22
2 xx [] xx log2)1011log( [] 2log)4log()1log()23log( xxx
[] )406(log1log 1010 xx [] )3log(2log3log)3log( xxx [] 1)203(loglog2 1010 xx
5 1
3 12
2
82
x
x
xx
x
125
1
5
51
22
1
2
1
57
3
xx
x
26552 xx
xxxx 96464392 11
211 3923 xxx
5
3
3 2
162
2
x
x
x
x
x
279
31
3 2
7
425 21
xxx
402421241 xx
1221 52355233 xxxxxx 8233 22 xx
01) )3log()2log( xx []
2log6 x [] xx 3log2log [] xlog26log [] 2log6log x
02)
2)1(log2
1 x [] 3x [] 1x []e pamundur [] 3
1x
03) )log()log( 22 baba [] ba log2 [] ba log [] ba log [] ba
ba
log2
04) 43 logloglog cba []
cba log4
1log
3
1log
2
1
[] 3
4
logb
ca
[]cba log
4
1log
3
1log
2
1
[]4
3
logc
ba
05) abba xx 2:
[]ax
[]abx 3
[]bax 3
[]ax3
06) 2loglog aa
[]e pamundur []3log a [] a
1log
[] alog
07) 21243 xxx [] 3x [] 4x [] e pamundur [] 2x
08) 131 2:8 aa
[] 32 []
a42 []16 []a32
09) zyx 8:42
[] zyx 322
[]zyx 2 []
zyx 34 []
z
yx
3
2
2
11) x27log
3 [] 5x [] 2
3x
[] 6x [] 3x
12) x8log3 2
[] 2
9x
[] 8
1x
[] 16
1x
[] 16x
13) 2
1log
2
1 x [] 2
1x
[] 2
1x
[] 2
1x
[] 2x
14)
2log4
1 x [] 8x [] 8
1x
[] 16x [] 2
15) x22log 2 [] 4
3x
[] 3
4x
[] 2
3x
[] 2
1x
16) ...9log3 x
[] x [] x2 []1 [] 2
17)
...2
1log
2
1
[] 0 [] e pamundur []1 [] 1x
18) 32log x
[]
6
2
1x
[]6 2x [] 2x [] 6
1x
19) aa 255 [] nuk transformohet []
35 [] aa 515 []a35
20) 4
1
4
1log x
[] 128
1x
[] 256x [] 256
1x
[]
8
2
1x
01) 3
1
2
1
4
3
xxx []19 12x []
12 7xx []xlog
12
19
[]x
12
19log
02)
2)1(log2
1 x
[] 3x [] 1x [] e pamundur [] 3
1x
03) 7 01,0log
[]10log
7
2
[]10log
2
7
[]10log
7
2
[]10log
2
7
04) 43 logloglog cba
[]cba log
4
1log
3
1log
2
1
[] 3
4
logb
ca
[]cba log
4
1log
3
1log
2
1
[]4
3
logc
ba
05) abba xx 2:
[]ax
[]abx 3
[]bax 3
[]ax3
06) 2loglog aa
[] e pamundur []3log a [] a
1log
[] alog
07) 21243 xxx [] 3x [] 4x [] e pamundur [] 2x
08) 131 2:8 aa
[] 32 []
a42 []16 []a32
09) zyx 8:42 []
zyx 322 []
zyx 2 []zyx 34 [] z
yx
3
2
2
10) )3log()2log( xx [] x5log [] xlog5 []
26log x [] xlog)5log(
11) x27log
3 [] 5x [] 2
3x
[] 6x [] 3x
12) x8log3 2
[] 2
9x
[] 8
1x
[] 16
1x
[] 16x
13) 2
1log
2
1 x [] 2
1x
[] 2
1x
[] 2
1x
[] 2x
14)
2log4
1 x
[] 8x [] 8
1x
[] 16x [] 2
1x
15) x22log2 [] 4
3x
[] 3
4x
[] 2
3x
[] 2
1x
16) ...9log3 x
[] x [] x2 [] 2
3x
[] 2
1x
17)
...2
1log
2
1
[] 0 [] e pamundur [] 2
3x
[] 1x
18) 32log x []
6
2
1x
[]6 2x [] 2x [] 6
1x
19) aa 255 [] nuk transformohet []
35 [] aa 515 []a35
20) 4
1
4
1log x
[] 128
1x
[] 256x [] 256
1x
[]8
2
1x
a)
5log3log1log2
1
2
1
2
1 xx
b) 3log112log1log 222 xx
c) 112log3log1log 222 xx d)12226 xx
a)
31
23
1
x
x
b) 1652 xxx c)
3log5log1log2
1
2
1
2
1 xx
d)
13
3
12
xx
e)
31
23
1
x
x
f)
3log5log1log2
1
2
1
2
1 xx
2)2(log1)1(log 55 xx 1)7(log)3(log4
1
4
1 xx 2)9(log)5(log222
xx
13 xLogLogx )62(log)9(log)1(log 333 xxx 42
3
4
5
LogxLogx
2)(log 2
3
1 xx xxx log2)32log()2log( 4
7
3log
6
1log2
5log22
44
4
xx
x
2)2(log1)1(log 55 xx 1)7(log)3(log4
1
4
1 xx 2)9(log)5(log222
xx
13 xLogLogx )62(log)9(log)1(log 333 xxx 42
3
4
5
LogxLogx
2)(log 2
3
1 xx xxx log2)32log()2log( 4
7
3log
6
1log2
5log22
44
4
xx
x
23
8
1
2
1
xx
xLogxLogLogx 12)1( 6215 LogxLogxLogx
2024 xx 2)1107( 2 xxLog 0352 2 LogxLogx
xx 21164 2
153 2 xx 25log2 xy
523 1 xx 8233 22 xx255 2 x
x
1)1(log)2(log 22 xx 12 3 xy 32log2
1 xy
xx
x
57
33
1
x
x
x
279
31
3 2
3
2
33
13232
2
xx
xx
xxx 2
423 6522 33 xxx
x 11
8122
6416
27242 xxxx
x
125
1
5
251
1
3332
1331
24
12
4
1
x
xx
x
823 13 xx 2022 31 xxx
x
721
77
4
1 2
4 2 20x x 2 8135
3x x 1244
12
xx
823 13 xx
243
89333 311 xxx
3 3 3 5 2 5 2 52 1 2 1x x x x x x
log( ) log( ) log2 1 2 x x 1)3(log2)2(log 22 xx 02log17log2 32
22 xx
xxx 11 428 □ 3
10x
□ 3
10x
□ 3
10x
□ 3
10x
1039 1 xx □ 3
5logx
□ 3log
5logx
□ 3
5x
□ pamundur
1211 2525 xxxx □ 8
125log
5
2log
x
□ 5
2log
8
125log
x
□ 2
5log
8
125log
x
□ 8
25log
5
2log
x
2log)11log()8log( xx □ 98 x □ 109 x □ 118 x □ 108 x
1)2(log)3(log2 22 xx □ 2
52 x
□ 3x □ 42 x □ 4x
27242 xx 63 13 x
7222 21 xxx
4 23 12 82 xx
1222 2323 xxxx 279 12 x
30255 xx
132 xx 027349 1 xx
5 16 1 93 xx
1113 3232 xxxx 273 32 x
5
3
3 2
322
2
x
x
□ 5
11
□ 5
11
□ 11
5
□ 11
5
3322 14 xx □ 1;4 □ 1;4 □ 1;4 □ 1;4
x
xx
7
625 23
□ 140log8
3log
□ 140log4
3log
□ 140log9
6log
□ 140log3
4log
135435 xxx □ 5
3log
3
4log
□ 3
4log
5
3log
□ 3
5log
3
4log
□ 5
3log
4
3log
)54log()1log()1log( xxx □ 2;2 □ 2 □ 2;0 □ 0
)2log()2log()2log(2)12log( 2 xxxxx
2log)5(log 22
2 xx [] 5;1 [] 5
[] 5 [] 1 xx log2)1011log( [] 1 [] 10;1 [] 10 [] 10/11 2log)4log()1log()23log( xxx [] 2;1 [] 2 [] 1 [] )406(log1log 1010 xx [] 0 [] 10 [] 10 []
)3log(2log3log)3log( xxx [] 323 [] 233 [] 233 [] 323
1)203(loglog2 1010 xx [] 20;10 [] 10 [] 20 []
Risultato1) 2)2(log1)1(log 55 xx
2) 2)3(log)2(log 22
2 xxx
3) 1)7(log)3(log
4
1
4
1 xx
4) 2)9(log)5(log2
22 xx
5) )6(log)5(log)1(log 333 xxx
6) 1)5(log)32(log
3
1
3
1 xx
1) )62(log)9(log)1(log 333 xxx
2) 2)1(log1)3(log 55 xx
3) 1)7(log)32(log
6
1
6
1 xx
4) 2)4(log)5(log 22
2 xxx
5) 2)1(log2)5(log
33 xx
6) 1)17(log)6(log
7
1
7
1 xx
12log x
)8log(
1)
5
3
3 2
162
2
x
x
5 1
3 12
2
32
x
x □ 16
71
□ 25
49
□ 16
49
□ 49
71
2) x
x
x
279
31
3 2
xx
x
125
1
5
251
1
□ 14
2
□ 9
5
□ 5
9
□ 7
2
3) 6522 33 xx 922 12 xx
□ 3;3 □ 1;3 □ 2;1 □ 3;1
4) 2022 31 xx 322 32 xx
□ 1 □ 1 □ 2 □ 2
5) x
xx
7
425 21
xx
x
57
33
1
01) )log()log( baba [] )log( 22 ba []
2)log( ba [] 22 loglog ba []
02) ba log2log [] ablog4 [] ablog2 []
44log ba [] 2log ab
03) 4
1log
2
1
[] –2 [] 2 [] 2
1
[] 4
1
04) xxx log2loglog3 []
3log x [] 0 [] 5log x []
4log x
05) [] 2log14log x [] )6log()2log( x [] 12loglog x [] 2log24log x
06) 3 2log aa
[] 3
2
[] 2
3
[] 3a [] 3
07) [] 12log20log [] )6log()2log( [] )8log(1log []
08) 1 13 x x
[] 2)1(3 x
[] 3 [] 0 [] 1
09) )log(log ba [] )log( ab []
)log(b
a
[])log(b
a
[] asnjera
10) 13:3 xx
[] xx 2
3 [] 13 xx
[] 3 [] x3
11) ba 3log2log [] ab6log [] [] ab5log [] )32log( ba
12) 8
1log125log 25 [] 6 [] 1 [] 0 [] asnjera
13) 2)135( [] 35 []
215 [] 29 []
25
14)
xx
ba
2:
3
[] a
b
2
3
[]
x
a
b
3
2
[]
x
a
b
2
3
[]
x
ab
6
15) xlog [] x<0 [] nuk ekzis [] x>0 [] x#0
16) b1000:10 []
b3110 []
b3110 []
b310 [] nuk modifik
17) 2)2(log4 x [] 14x [] 9x [] 15x [] 17x
18) a
b
2 []
b a2 [] b
a
2
1
[] a
b
2
1
[] b
a
2
2
19) 11 2:8 xx
[] 12 x []
14 x []
110 x []
116 x
20) yx aa
[] yxa []
x
y
a
a
[] )( yx [] asnjera
01) )log()log( baba □ )log( 22 ba □
2)log( ba □ 22 loglog ba □ asnjera
02) ba log2log2 □ ablog4 □ ablog2 □
44log ba □ )log( 22 ba
03) 2
1log4log
2
1
2
1 □ –2 □ 1 □ 3 □ 1
04) xxx log2loglog3 □
3log x □ xlog □ 5log x □
4log x
05) 58 x □ 5log8log x □ 5log
8logx
□ 8
5x
□ 8log
5logx
06) 3log aa
□ 3
2
□ 2
3
□ 3a □ 3
07) 877 1 xx □ 3x □ 2x □ 1x □ 1x
08) 11 5:3 xx
□
2)1(
5
3 x
□
1
5
3 x
□
1
5
3
x
□
1
3
5 x
09) )3log(log xx □ )2log( x □ )3log( x □ 3
1log
□ asnjera
10) 13:3 xx
□ xx 2
3 □ 13 xx
□ 3 □ x3
11) )3log()2log( xx □ x6log □ )6log( x □
26log x □ asnjera
12) 11 22 xx
□ 1
1
2 x
x
□ 4 □
x22
3
□
4
1
13) 3)(log)(log yxyx aa □ )(log 22 yxa □ )(log 33 yxa □ )(log2 yxa □ )(log 33 yxa
14)
xx
ba
2
:3
□ a
b
2
3
□
x
a
b
3
2
□
x
a
b
2
3
□
x
ab
6
15) )log(log yx □e pamundur □ )log( xy □ y
xlog
□
xy
1log
16) 333 352
□
3
3
52
□ 973 □ 3)352( □ 106
17) 2)1(log3 x □ 8x □ 5x □ 1x □ 3x
18) a
b
2 □
b a2 □ b
a
2
1
□ a
b
2
1
□ b
a
2
2
19) 11 28 xx
□ 12 x □
14 x □
110 x □
116 x
20) yx aa □
yxa □
xya □ yx □ asnjera
01) yx aa loglog □ )(log yxa □ y
xalog
□ x
yalog
□ xyalog
02) )(log baa □ ba aa loglog □ aa ba loglog □ balog1 □ asnjera
03) 1log2log 44 □ –2 □ 2
1
□ 2
1
□ 2
04) 33 3log2log
□ 3
2log3
□ 2
3log3
□ 3
2log2
□ 2
3log2
05) a
b
2 □
b a2 □
b
a
2
1
□
a
b
2
1
□ a b2
06) 2log aa □ 1 □
2a □ 0 □ 2
07) yxyx aa 2: □
xa 3 □
yxa □
xa3 □
ya
08) 11 53 xx
□ 2)1(15 x
□ 115 x
□ 2215 x
□ 18 x
09) )log(log xx □ )log( 2x □
2)log( x □ 0 □ asnjera
10) 33 3:2
□
3
3
2
□
3
2
3
□ 9
4
□ 36
11) baba 2:2 □
22
2 ba □
b22 □ b22
□ a22
12) 11 22 xx
□ )1)(1(2 xx □
x22
5
□ 1 □ x22
13) 3)(log)(log yxyx aa □ )(log 22 yxa □ )(log 33 yxa □
4)(log yxa □ )(log 33 yxa
14) )log()log( baba □ )log( 22 ba □ 22 loglog ba □
2)log( ba □ 2)log( ba
15) 11 : xx aa
□ 12 xa □
1
1
x
x
a □ 2a □
2xa
16) 333 352
□
3
3
52
□ 100 □ 3)532( □ 106
17) 1log3log 22 □ 4log 2 □ 3log2 □ 1log2 □ 2log2
18) xx log)1log( □ )12log( x □ )1log( □ x
x 1log
□ 1log
xx
19) )log()log( baba □ a2log □ b2log □ ba
ba
log □ )log(
)log(
ba
ba
20) 3log22log3 32 □ 36log6 □ 5 □ 6 □ 6log6
21)
xx
ba
1
:1
□ a
b
□ b
a
□
x
a
b
□ xab)(
22) )log()log(2 baba □ )log( ba □ )log( 22 ba □ )log( 22 ba □
23) 35 x □ 5log3log x □ 5log
3logx
□ 3log5log x □ 3log
5logx
23) 3)1(log 2 x □ 7x □ 5x □ 1x □ 3x
24) xx log)1log( □ 2
1x
□ 0x □ 1x □ asnjera
25) yxyx 22
□ 22
2 yx □
y22 □ yx
yx
2 □ )12(
2
2 2 yy
x
26) yx aa
□ yx □ y
x
a □ yxa
□ asnjera
27) zyx 101010 □
zyx 10 □ xyz10 □
xyz1000 □ asnjera
28) xx aa 2loglog □ )(log xa □ xalog □ 2
1log a
□ asnjera
29) 11 22 xx
□ )1)(1(2 xx □
22 □
x22
5
□ x22
30) 11 2:8 xx
□ 12 x □
14 x □
16 x □
04
31) 1log2log 88 □ 3 □ 3
1
□ 3
1
□ 3
32) 11 : xx aa
□ a □ xa 2
□2
1
a □ 2a
33) 5log225log □ 0 □ 1 □ 5log □ 10log
34) )log()log( yx □ □ xylog □ y
xlog
□ xy
1log
35) ba log2log3 □ )23log( ba □ ab6log □
ba23log □ 23log ba
36) ba log
2
1log
3
1
□ b
a3
log □ 6
logab
□ 6logb
a
□ )log(3 ba
37) xx loglog2 3 □ 4log2 x □
7log x □ 10log x □
5log x
38) 22 loglog ba
□
2
log
b
a
□
2
log
a
b
□ )(log baba □ )log(log baba
39) xx 222 □ )21(2 xx □
32 □ 222 x
□
40) yx 22 □
xy2 □ yx2 □ )(2 yx □
41) 1 13 x x
□ 1
1
3 x
x
□ 1
1
3 x
x
□ 1
1
3
3
x
x
□ 1
1
3
3
x
x
42) 1loglog x □ □ xlog □ 0 □ )1log( x
43) yx 3log3log □
yx3log □ 7log x □
10log x □ yx 33log
44) )4log()3log( □ □ 12log □ 12
1log
□ )7log(
45) xx
1loglog
□ □ 0 □
xx
1log
□ )1log( x
46) a
b
2 □
b a2 □
b
a
2
1
□
a
b
2
1
□ b
a
2
2
47) 2024 xx □ 3x □ 2x □ 1x □ 1x
48) )log()log( baba □ )(21 baog □ )log( 22 ba □ a2log □ ba
ba
log
49) xx 3log5log □ 1251ogx □ 81ogx □
15log x □ x15log
50) 3
1
3
1
2:3 □
3)5.1( □ 3 6.0 □
3 5.1 □ 2
3
1.12226 xx
2.xx 21164
3. 255 2 xx
4. 2log)11log()8log( xx
5. 1)2(log)3(log2 22 xx
6. )54log()1log()1log( xxx
7.)2log()2log()2log(2)12log( 2 xxxxx
8. 2)2(log1)1(log 55 xx
9. 2log)5(log 22
2 xx 10. xx log2)1011log( 11. 2log)4log()1log()23log( xxx
12. )406(log1log 1010 xx
13. )3log(2log3log)3log( xxx
14. 1)203(loglog2 1010 xx
