Question

2ka power 2x+1=4ka power 2x-1​

Answer 1

Step-by-step explanation:

2'2x-1 = 4 can be written as 2'2 (2x-1)

Since in both expression 2 is same so we can write it as

2x-1 = 2(2x-1)

2x-1 = 4x -4

3 = 2x

X = 3/2

Answer 2

Correct Question :-

If 2^(2x + 1) = 4^(2x - 1) then find the value of x.

Answer :-

Value of x is 3/2.

Explanation :-

2^(2x + 1) = 4^(2x - 1)

⇒ 2^(2x + 1) = (2²)^(2x - 1)

[ ∵ 4 = 2²]

⇒ 2^(2x + 1) = 2^{2(2x - 1)}

[ ∵ (aᵐ)ⁿ = aᵐⁿ ]

⇒ 2^(2x + 1) = 2^(4x - 2)

⇒ 2x + 1 = 4x - 2

[ ∵ aᵐ = aⁿ then m = n ]

⇒ 1 + 2 = 4x - 2x

⇒ 3 = 2x

⇒ 3/2 = x

⇒ x = 3/2

∴ the value of x is 3/2.