Scroll:Logarithms >> Find the value and solve the equation >> saq (4211)


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 = 168 = 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  8x54

= 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

 log6
 
 (x+4) =1 
 (x-1)

 

 log6
 
 (x+4) ,61 
 (x-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]

5(5x+1) = 210(x+5)

⇒ 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]

5(5x+1) = 210(x+5)

⇒ 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 = 168 = 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  8x54

= log1010 = 1