Soal Logaritma

Logarithm Problems Solve these following problems briefly and clearly! log a 1. Given a=0,666... and b=0,444..., value of = ... log b

a.

1 4

c.

1 2

b.

1 3

d. 2

e. 3

5

2. If  log 2 = x then log 2,5 = …. a. b.

1- x

c.

1+ x 1+ x

d.

1 -x

a

1 - 2x

e.

1 -x 1 + 2x

1 +x 1 - 2x

1 +x

a

a

3. The value a of  log 16 - 3 log 4 + log 32 = 3 is …. a. 6 c. 4 e. 2 b. 5 d. 3

4. The simple form of 9 log( x −  y )− 9 log( x 2 −  y 2 ) is ... . a. - 9 log (x+y) b.

9

log (x+y)

c.

9

log (x-y)

5. The simple form of 

27

a. 1 b. 2

7. If log

m n

9

e. log (x-y)

25

log 125. log

1 5

log 10

+

1 25

a. 4 b. 2

8

64

+

1 9

is ... .

log 100

1 64

c. 3 d. 4

= 9 , then log

log

e. 5

log 1000

is ... . e. 5

3

3

1

c. 3 d. 4

6. The value of  a. 1 b. 2

d. 9 log (-x+y)

3

c. 0 d. -2

n

2

m2

is ... . e. -4

a

b

8. If  log b + log a = 2 then the correct relationship is .… 2 2 a. a + b = 1 d. 2a - b = 0 b. a - b = a + b e. 2b = a c. a - b = 0 ⎛  2 log 5 + 3 log 5  ⎞ 36 ⎟ ⋅ log 0,2 is … ⎜ log 5 x 3log5 ⎟ ⎝   ⎠

9. The value of  ⎜ 2 a. 1

c. - 12

b. -1

d. log 2

2

6

e. log 3

6

2

2

10. Given log 3 = a and log 7 = b then log 63 = .… a. 2a + b c. 2b + a e. -2b+a b. 2a - b d. -2a+b 11. If

2

3 log( x + ) = 2 , then value of x is … .  x a. 1 or 4 c. 1 or 3 b. -1 or 4 d. -1 or 3 2

12. If log x -logx + log a. 1 b. 10

 x = 6 then x = … . c. 100 d. 1000

13. Solution Set of the equation ( ( 5 log x) 2 = 9 is ... . 1 a. {125} c. { ,125 } 125 1 b. {243} d. { ,243 } 243

e. -3 or 1

e. 10000

e. {-125,125}

3

− 14. Solution of the equation (9 log(3 x 2 ) = 16 is ... . 2 2 a. { } e. {- ,2} 3 3 2 b. {2} d. { ,2} 3

7

7

e. {-2,

2 3

}

15. Solution of the equation log (x + 1) + log (x - 5) = 1 is …. a. -2 c. 6 e. -6 or 2 b. 2 d. -2 or 6