If 2^x − 2^x−2 = 192, the value of x is

Given 2^x − 2^x−2 = 192

⇒2^x–2^x.2⁻² = 192

Taking 2^x common from both the terms,

⇒2^x (1 - 2⁻²) = 192

For a number a ≠ 0and natural number n, we define

⇒2^x = 64× 4

⇒2^x = 2⁶ × 2²

For any a ≠ 0, and integers m,n, a^m × aⁿ = a^m+n

⇒2^x = 2⁸

Hence, x = 8