Direction: Study the following questions carefully and choose the right answer.
1
If 22n−1    =  1   , then the value of n is:
  8n−3  

» Explain it
B
22n−1
 =  1
8n−3
1
(23)n−3
 =  1
23(n−3)
 =  1
2(3n−9)

= 2(9−3n)

Let's take power from the equation:

2n−1 = 9−3n

⇒ 5n = 10  

⇒   n = 2.

Hence, option B is correct.

2
If    9n x 35 x (27)3    =  27,   then the value of n is :
3 x (81)4  
» Explain it
C
9n x 35 x (27)3
3 x (81)4

= 27 ⇔  (32)n x 3x (33)3
3 x (34)4

= 33 ⇔  32n x 3x 3(3x3)  =  33
3 x 3(4x4)

⇔  32n+5+9
3 x 316

= 33  ⇔  32n+14
317

= 33 ⇔  3(2n+14−17) = 33

⇔  32n – 3 = 33

From the equation powers :

⇔ 2n – 3 = 3 ⇔ 2n = 6 ⇔ n = 3.

Hence, option C is correct.

3
If 2n+4 – 2n+2 = 3, then n is equal to: 
» Explain it
D
Given expression :

2n+4 − 2n+2 = 3  ⇔ 2n+2 (2− 1) = 3  ⇔  2n+2   = 1 = 20

[Bcz 20  ​is equal to 1]


From the equation power :    
                                        
⇔ n + 2 = 0 ⇔ n = − 2

Hence, option D is correct.

4
If 2n-1 2n+1 = 320, then n is equal to:
» Explain it
D
Given equation :

2n−1 + 2n+1 = 320  

⇔  2n−1(1+22) = 320

⇔ 5 x 2n−1= 320

⇔ 2n−1 = 320 / 5

 = 64 = 26   

From the eqution power :

⇔ n−1 = 6 ⇔ n = 7.

Hence, option D is correct.

5
If 3x  3x – 1 = 18, then the value of xis:
» Explain it
C
From the given expression :

3x − 3− 1 = 18  

⇔ 31 (3 − 1) = 18  

⇔  3x −1 = 9 = 32

From the equation power :

  x − 1 = 2 ⇔ x = 3.

∴ xx = 33 = 27

Hence, option C is correct.