32x - 3x - 72 = 0 হলে, x- এর মান কত?

3^2x - 3^x - 72 = 0 হলে, x- এর মান কত?

A 2

B 3

C 6

D 8

Solution

Correct Answer: Option A

3^2x - 3^x - 72 = 0
⇒ (3^x)² - 3^x - 72 = 0
⇒ (3^x)² - 9 . 3^x + 8 . 3^x - 72 = 0
⇒ 3^x(3^x - 9) + 8(3^x - 9) = 0
⇒ (3^x - 9) (3^x + 8) = 0
[3^x + 8 ≠ 0]
⇒ 3^x - 9 = 0
⇒ 3^x = 9
∴ x = 3

Solution

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