Logaritma

A collection of quizzes
Questions and answers

Q2 SPL 1

INSTRUCTION: ANSWER ALL THE QUESTIONS [CLO1:C2]
1. Simplify the following logarithm expressions into the simplest form:

a. 2 log34 + log32 - 2 b. 3 − 525

= 342 + log 32 – 2 log33 = 3 55 - 5 25

= log316 + log32 – log39 = 5125 − 525

= log3 (16 2) = 5(12255)
= 55
9
=1
= 3(392)

2. Find the value of x for equation 23 − 2( − 1) = 3

23 − 2( − 1) = 3
23 − 2( − 1) = 3 22

2( 3− 1) = 223
3 = 8

−1

3 = 8 − 8
= 8

5

Q2 SPL 2

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify the following logarithm expressions into the simplest form:

c. 5( + ) − 2 d. 3 42 + 43 − 46
= 5( + ) − 2 55 = 423+ 43 - 46
= 5( + ) − 552 = 48 + 43 − 46

= 5 ( + ) = 4 (8 3)
25 6

= 44

=1

2. Find the value of x for equation 24 + 25 = 2

24 + 25 = 2 22

24 + 25 = 222

2(4 )(5) = 24

220 = 24

∴ 20 = 4

= 4
20
1
= 5

Q2 SPL 3

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify each of logarithm expression below into the simplest form :

e. 464 + 4 3 2 − 44 f. 2 5 − 1 + 5 3

= 4 (64 x 3 2) = 5 2 − 55 + 5 3
( 2
4 = 5 x 3 )
5
= 416 3
5
= 5 5

2. Find the value of x

2 2 − 236 = 2 22

2 2 − 236 = 222

2 ( 2) = 24

36
( 2) = 4

36

= 12

Q2 SPL 4

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify each of logarithm expression below as a single logarithm.

g. 39 + 38 − 36 h. 2 log − 3 + log( + 1)

= 4 (9 x 8) = log 2 − 103 + log( + 1)
6
= 2( +1)
103
= 312

= 3+ 2
100

2. Find the value of x for the following equation.

3(2 − 1) + 34 = 5
3(2 − 1)4 = 5

8 − 4 = 35
8 = 243 + 4

= 247 @ 30.875

8

Q2 SPL 5

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify the following logarithm expressions into the simplest form :

i. 525 j. 4 log + − 2log a

2

= 552( ) 1

= (2 ) 55 = 4 + 2 − log 2
= 2
= 25

= 5 log

2

2. Find the value of x for equation 28 − 2(2 − 1) = 3 .

28 − 2(2 − 1) = 3
8
2 (2 − 1) = 3
8
2 − 1 = 23

18
2 − 1 = 8

1 = 2 − 1
= 2

2

= 1

Other solution:

28 − 2(2 − 1) = 3
223 − 2(2 − 1) = 3 22
223 − 2(2 − 1) = 223
223 − 223 = 2(2 − 1)
23
2 23 = 2(2 − 1)

1 = 2 − 1

= 2

2

= 1

Q2 SPL 6

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify each of logarithm expression below as a single logarithm:

k. 2 + 3 2 − 2 l. 1 log 81 − 3log
2

Solution : Solution

= 2 + 3 2 3 − 2 1

3 = (81 )2 − 3

= 9√ − 3

= 2 9√
3
=

2. Find the value of x for equation:

225 = 3 + 2( − 1) .

Solution:

225 = 3 + 2( − 1)
225 = 223 + 2( − 1)
225 = 28( − 1)

25 = 8 − 8
8 = 33

= 33 @ 4.125

8

Q2 SPL 7

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify each of logarithm expression below into the simplest form:

m. 3245 n. 381 − log39 + 1 33
2
Solution :
= 335 Solution
= 5 33
=5 = 3 (81) + 1
2
Other solution 9
log 243 1
= 33 + 2
= log 3 1
=5 = 33 + 2
1
=1+2
3
=2

2. Find the value of a for the equation:

2 + 25 = 4

Solution:

2( + 5) = 4

5 = 24
= 24

5

= 16

5

Q2 SPL 8

INSTRUCTION: ANSWER ALL THE QUESTIONS

1. Simplify each of logarithm expression below into the simplest form:

o. 3245 p. 381 − log39 + 1 33
2
Solution :
= 335 Solution
= 5 33
=5 = 3 (81) + 1
2
Other solution 9
log 243 1
= 33 + 2
= log 3 1
=5 = 33 + 2
1
=1+2
3
=2

2. Find the value of a for the equation:

2 + 25 = 4

Solution:

2( + 5) = 4

5 = 24
= 24

5

= 16

5