EXERCISES

1. Calculate:

a) log216 = b) log416 =

c) log5125 = d) log81 =

e) log88 = f) log101 =

2. What number is n?

a) log10n = 3

b) 5 = log2n

c) log2n = 0 d) 1 = log10n

e) logn 1

16 = 2

f) logn

1

5 = 1

g) log2 1

32 = n h) log2

1

2 = n

3. Calculate:

a) log9 1

9 =

b) log9 1

81 = c) log2

1

4 =

d) log2 1

8 = e) log2

1

16 =

f) log10 .01 = g) log10 .001 =

h) log6 = 1/3 i) logb = 3/4

4. Calculate:

a)

b)

5. If log 3 = 0.477, calculate:

a) log 30

b) log 300

c) log 3000

d) log 0.3

e) log 0.03

f) log 0.003

g) log 0.9

6. Calculate:

a) log2 4 =

b) log3 27 =

c) log2 16 =

d) log5 125 =

e) log3 243 =

f) log2 0,5 =

g) log2 0,25 =

h) log2 0,125 =

i) log6 216 =

j) log 1000 =

7. Solve using logarithm properties.

a) log (53) =

b) log (23 . 3) =

c) log (7 : 3) =

d) log (2 . 3 : 4)5 =

8. Change de base:

a) log2 5 = c) log3 7 =

b) log32 = d) log5 24 =

9. Calculate the value of x:

a) log1/2 32 = x

b) 9x+27 = 4.3

x+1

10. Calculate:

a) log 3 27 + log

3 1 =

b) log 5 25 log

5 5 =

c ) log 4 64 + log

8 64 =

d) log 0,1 log 0,01 =

e) log 5 + log 20 =

f) log 2 log 0,2 =

g) log 32 / log 2 =

11. Calculate the value of x:

a ) log 2 x = 3

b) log 7 x = 3

c) log 6 [ 4 ( x 1 ) ] = 2

d) log 8 [ 2 ( x

3 + 5 ) ] = 2

e) log x 125 = 3

f) log x 25 = 2

g) log 2 x + 3

81 = 2

12. Calculate:

a)

b)

c)

d)

e)

f)

g)

)3(log81

)33(log3

9

3log

4

3

3log81

3

3log81

9

3log

4

9

1

81log3

3

13. If log 2 = 0,3010 and log 3 = 0,4771. Calculate:

a) log 36

b) log (9/4)

c) log 5

14. Expres with one logartihm:

a) log x + log y

b) log (x . y) log z

c) 2 log x + 3 log y

d) log x 5 log y + 2 log c

e) log x log y

f) log x 4 log y +2 log z +1/3 log t log k

15. If log k = 0.5 and log t = 0.31, calculate:

a)

b)

c)

16. Change the base and calculate with calculator:

a)

b)

c)

d)

e)

t

k 2log

)log( 3tk

3

210log

t

k

15log8

6log2

1

32log15

25ln

32log 2

17. If log(2) = a, log(3) = b and log(7) = c, calculate:

a) log(4) =

b) log(6) =

c) log(8) =

d) log(9) =

e) log(14) =

f) log(21) =

g) log(5) =

h) log(15) =

i) log(1.5) =

j) log(0.5) =

k) log(0.2) =

l) log(12) =

18. Calculate x:

a) x = log8(16)

b) -3 = log3(x)

c) (4/3)=logx(102/3

)

d) -3 = 2log25(x)

e) x = log8(25) + log7((1/49)1/3

)

f) log5(100)+log3(4) = x

19. Solve the following equations:

a) 2 log(5x - 4) - log 4 = log (x + 4)

b)

c)

d)

e)

f)

g)

350loglog x

32log)3log(5 x

)310log(log2 xx

1)6log()3log( xx

xx log2)9log(

1log53log xx