Written Instructions:
For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..
For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.
Leave your answers in the simplest form or correct to two decimal places.
1) Solve the equation in each of the following. log48(log2x) = 2
Answer:_______________ |
2) Prove the following equations log101600 = 2+4log102 Answer:_______________ |
3) Solve the equation in each of the following. log4(x+4) + log48-2 = 2
Answer:_______________ |
4) Solve the equation in each of the following. log108 + log105 - log104
Answer:_______________ |
5) Solve the equation in each of the following. log6(x+4) - log6(x-1) = 1
Answer:_______________ |
6) Solve the equation in each of the following. log105 + log10(5x+1) = log10(x+5)+1
Answer:_______________ |
7) Solve the equation in each of the following. log48(log2x) = 2
Answer:_______________ |
8) Prove the following equations log101600 = 2+4log102 Answer:_______________ |
9) Solve the equation in each of the following. log4(x+4) + log48-2 = 2
Answer:_______________ |
10) Solve the equation in each of the following. log108 + log105 - log104
Answer:_______________ |
1) Solve the equation in each of the following. log48(log2x) = 2 Answer: 4 SOLUTION 1 : log48(log2x) = 2 ⇒ 8(log2x) = 42 = 16 [ Exponential form] ⇒ log2x = 42 = = 2 ⇒ log2x = 2 ⇒ x = 22 = 4 |
2) Prove the following equations log101600 = 2+4log102 SOLUTION 1 : L.H.S = log101600 = log10(16x100) = log1016+log10100 = log1024+log10102 = 4log102+2log1010 = 4log102+2 L.H.S= R.H.S |
3) Solve the equation in each of the following. log4(x+4) + log48-2 = 2 Answer: -2 SOLUTION 1 : log4(x+4) + log48-2 = 2 ⇒ log48(x+4) =2 ⇒ 8(x+4) = 2 ⇒ 8(x+4) 16 ⇒ 8x + 32 - 16 ⇒ 8x -16 x = -2 |
4) Solve the equation in each of the following. log108 + log105 - log104 Answer: 1 SOLUTION 1 : log108 + log105 - log104 = log10 = log1010 = 1 |
5) Solve the equation in each of the following. log6(x+4) - log6(x-1) = 1 Answer: 2 SOLUTION 1 : log6(x+4) - log6(x-1) = 1
⇒ x+4 = 6(x-1) = 6x-6 ⇒ 5x = 10 ⇒ x = 2
|
6) Solve the equation in each of the following. log105 + log10(5x+1) = log10(x+5)+1 Answer: 3 SOLUTION 1 : log105 + log10(5x+1) = log10(x+5)+1 ⇒ log105(5x+1) = log10(x+5)+log1010 = log10(5+1) [Remove log on both sides] ⇒ ⇒ 5x+1 = 2x+10 3x = 9 ⇒ x = 3 SOLUTION 2 : log105 + log10(5x+1) = log10(x+5)+1 ⇒ log105(5x+1) = log10(x+5)+log1010 = log10(5+1) [Remove log on both sides] ⇒ ⇒ 5x+1 = 2x+10 3x = 9 ⇒ x = 3 |
7) Solve the equation in each of the following. log48(log2x) = 2 Answer: 4 SOLUTION 1 : log48(log2x) = 2 ⇒ 8(log2x) = 42 = 16 [ Exponential form] ⇒ log2x = 42 = = 2 ⇒ log2x = 2 ⇒ x = 22 = 4 |
8) Prove the following equations log101600 = 2+4log102 SOLUTION 1 : L.H.S = log101600 = log10(16x100) = log1016+log10100 = log1024+log10102 = 4log102+2log1010 = 4log102+2 L.H.S= R.H.S |
9) Solve the equation in each of the following. log4(x+4) + log48-2 = 2 Answer: -2 SOLUTION 1 : log4(x+4) + log48-2 = 2 ⇒ log48(x+4) =2 ⇒ 8(x+4) = 2 ⇒ 8(x+4) 16 ⇒ 8x + 32 - 16 ⇒ 8x -16 x = -2 |
10) Solve the equation in each of the following. log108 + log105 - log104 Answer: 1 SOLUTION 1 : log108 + log105 - log104 = log10 = log1010 = 1 |