Direction: Study the following questions carefully and choose the right answer.
Important for :
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 35 x (33)3 3 x (34)4

 = 33 ⇔ 32n x 35 x 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.