JEE Main 2024 Mathematics question
The sum of all the solutions of the equation (8)²ˣ − 16·(8)ˣ + 48 = 0 is:
Answer: (C)
Solution
With t = 8ˣ: t² − 16t + 48 = 0 ⇒ t = 4 or 12, so x = log₈4 and log₈12. The sum is log₈48 = 1 + log₈6.
The sum of all the solutions of the equation (8)²ˣ − 16·(8)ˣ + 48 = 0 is:
With t = 8ˣ: t² − 16t + 48 = 0 ⇒ t = 4 or 12, so x = log₈4 and log₈12. The sum is log₈48 = 1 + log₈6.