РЕШЕЊА ЗАДАТАКА

1. а) 2xx3 3393x9log 2x

б) 1xx4 44

4

14x

4

1log 1x

в)

333

x 2

1x

8

1x3

8

1log

2

1x

г) x2

1x23xlog

33

2 8

1x

д)

x

4

1x

4

1

2

1xlog

2

1

4/1 2

1x

2. а) 142log42log16log 24

22 4

б)

12

7

5log2

7

5log

49

25log 7/5

2

7/57/5 2

в) 12

15log

2

15log5log 5

2

1

55 2

1

г)

14

2

1log4

2

1log

16

1log 2/1

4

2/12/1 4

д) 1225log225log25

1log

625

1log 25

22522525 2

ђ)

13

13log

3

2

2

13log

2

13log

2

19log 3

3

2

33 2

33

3 2

3

1

3. а) blogalog ablog

б) 2blogalogblog2alog2b

alog

в) 432 clogblogalogclog4blog3alog2 432 cbalog

г) 5 233 25

2

33

2

clogblogalogclogblogalogclog5

2blog3alog

3

2

5 2

33 2

c

balog

д) 322222 balogalogbalog3alog2

322

2

ba

alog

4. а) logb

a4A

2

blogalog22logblogalog4logbloga4logb

a4logAlog 222

2

blogalog22log2

б) logyx

xA

2

ylogxlog2

2

1ylogxlog2xlog

2

1ylogxlogxlogyxlogxlog

yx

xlogAlog 22

1

22

ylogxlog2

3

в) logbcaA 3

2

13

13 bclog

3

1alog

3

1bclogalog

3

1bcalog

3

1bcalogbcalogAlog

clogblog6

1alog

3

1bclog

2

1

3

1alog

3

1 clog

6

1blog

6

1alog

3

1

г) logcbaA

2

12

1

cblog2

1alog

2

1cblogalog

2

1cbalog

2

1cbalogcbalogAlog

2

1

clog4

1blog

4

1alog

2

1clogblog

4

1alog

2

1cblog

2

1

2

1alog

2

1

clog8

1blog

4

1alog

2

1

д) logxy

xyxA

3

xylog3

1xyxlog

2

1xylogxyxlogxylogxyxlog

xy

xyxlogAlog 3

12

13

3

ylog3

1xlog

3

1xylog

2

1xlog

2

1ylogxlog

3

1xylogxlog

2

12

1

ylog3

1xlog

3

1ylogxlog

4

1xlog

2

1ylog

3

1xlog

3

1xylog

2

1

2

1xlog

2

1

ylog

3

1

4

1xlog

3

1

4

1

2

1ylog

3

1xlog

3

1ylog

4

1xlog

4

1xlog

2

1

ylog12

43xlog

12

436ylog

12

1xlog

12

5

5. а) clog2alog3xlog 333

2

33

33 clogalogxlog

23

33 calogxlog = > 23cax

б) balog7

4balog

5

3xlog

7

4

5

3

balogbalogxlog

7 45 3balogbalogxlog

7 4

5 3

ba

balogxlog

=>

7 4

5 3

ba

bax

в)

dlog

2

1clog

3

1blogalog

2

1xlog

2

1

dlogclog3

1

b

alog

2

1xlog

dlogclog

3

1

b

alog

2

1xlog

dclog

3

1

b

alog

2

1xlog

3

1

dclogb

alog

2

1xlog

3 dclogb

alog

2

1xlog

3 dc

b

alog

2

1xlog

2

1

3 dcb

alogxlog

3 dc

b

alogxlog =>

3 dcb

ax

г)

clogblog

m

1alog

n

1xlog

c

blog

m

1alog

n

1xlog

m

1

c

blogalog

n

1xlog

m

c

blogalog

n

1xlog

m

c

balog

n

1xlog

n

1

m

c

balogxlog

n mc

balogxlog

n mc

bax

6. а) 1log4loglog14loglog2log4loglog2logloglog16logloglog 848482484

248248 0

б) 4log9log2log34log3log2log4log3log28log 66262

63

2662

1236log236log336log349log13 62

666 1

в) 3log3log

2log3log2log

3log

13log2log5log2log9log5log 2

5

525

5

2253543 2

2log

12log3log2log

3323 1

г)

2log31

12log1log

2

12log2loglog8log

2

1loglog 223

32

1232/129/1 12

2log2

131log

2

133

д) 6526

2log

152362log15 log3

2

10log6

log3

10

10log6

log310

log36 36

223696

1251565log

6 252

6 24

ђ)

22222

4

1

4

14284

4

1

4

1log

7log

5log

3log

49log

25log

81 7

335

2237125

9

44

2

12221222

24

1

4

14

log7

log5

log3

3log7

log5

log3

log7

log25

log3 75

3

2

7

2

53753

16644

2

322

е)

5

163

log25

log2

23

log5

log2

log3

log5 153

5

412535432253

5

2

2

5235

5

168

5

1635

5

1635 23

5

24

ж)

3log

53

2log3log5log3log

log5

log53

4log9log25log3log

224

9 3249/15

516

9 84 81

493

5

1

223

23

325

1

527

343

2log32299

3log

53

2log22981

3log

53

2log23log25log24912

5

3/12

4

3 25

4

5

1

3

5

433

15

6299

5

132

7. а) ?9log6 ; k2log6

2log26log22log6log4log36log4

36log9log 66

26

266666 k22

б) ?16log6 k2log12

2log12log

2log4

2

12log

2log

6log

16log16log

1212

12

12

412

12

126 k1

k4

в) ?125log ; k2log

2log10log32

10log35log35log125log 3 k13

г) ?6log5 ; b3log,a2log

2log10log

3log2log

2

10log

32log

5log

6log6log5 a1

ba

д) ?5log3 ; b5log,a2log 66

2log6log

b

2

6log

b

3log

5log5log

666

6

63 a1

b

ђ) ?28log35 ; b5log,a7log 1414

ba

a11

ab

7log14log1

7log5log

7

14log1

75log

2log14log

35log

214log28log 1414

1414

14

14

1414

14

1435 ba

a2

е) ?8log30 ; b3log,a5log

b1

5log10log3

1b5

10log3

10log3log

2log3

103log

2log

30log

8log8log

3

30

b1

a13