If 16x - 2 × 22x + 12 = 42x + 6, then find the value of x.1. 32. 43.

1.	If 16x - 2 × 22x + 12 = 42x + 6, then find the value of x.1. 32. 43. 54. 2
Answer» Correct Answer - Option 2 : 4 Given: 16x - 2 × 22x + 12 = 42x + 6 Concept Used: a^m × aⁿ = a^{m + n} If, x^p = x^q, then p = q Calculations: 16x - 2 × 22x + 12 = 42x + 6 16 = 2⁴, 4 = 2² ⇒ 24 × (x - 2) × 22x + 12 = 22 × (2x + 6) ⇒ 2^{(4x - 8)} × 22x + 12 = 2^{(4x + 12)} am × an = am + n ⇒ 2^{(4x - 8 + 2x + 12)} = 2(4x + 12) ⇒ 2⁽^{6x + 4)} = 2(4x + 12) Now, xp = xq ⇒ 6x + 4 = 4x + 12 ⇒ 2x = 8 ⇒ x = 4 ∴ The value of x is 4.

If 16x - 2 × 22x + 12 = 42x + 6, then find the value of x.1. 32. 43. 54. 2

Answer» Correct Answer - Option 2 : 4

Given:

16x - 2 × 22x + 12 = 42x + 6

Concept Used:

a^m × aⁿ = a^{m + n}

If, x^p = x^q, then

p = q

Calculations:

16x - 2 × 22x + 12 = 42x + 6

16 = 2⁴, 4 = 2²

⇒ 24 × (x - 2) × 22x + 12 = 22 × (2x + 6)

⇒ 2^{(4x - 8)} × 22x + 12 = 2^{(4x + 12)}

am × an = am + n

⇒ 2^{(4x - 8 + 2x + 12)} = 2(4x + 12)

⇒ 2⁽^{6x + 4)} = 2(4x + 12)

Now, xp = xq

⇒ 6x + 4 = 4x + 12

⇒ 2x = 8

⇒ x = 4

∴ The value of x is 4.