Solve : 3^(4x+1) - 2 x 3^(2x + 2) -81 = 0.

Question

Solve : \(3^{4x + 1} -2\times3^{2x+2}-81 =0.\)

Answer 1

\(3^{4x + 1} -2\times3^{2x+2}-81 =0\)

⇒ \(3\times3^{4x}-2\times3^2\times3^{2x}-81=0\) ⇒ \(3\times3^{4x}-18\times3^{2x}-81=0\)

⇒ 3a² - 18a - 81 = 0 ⇒ (Put 3^2x = a) ⇒ a² - 6a - 27 = 0

⇒ a² - 9a + 3a - 27 = 0 ⇒ a(a - 9) + 3(a - 9) = 0

⇒(a - 9)(a - 3) = 0 ⇒ a - 9 = 0 or a + 3 = 0

⇒ a = 9 or a = -3 ⇒ 3^2x = 9 or 3^2x = -3

⇒3^2x = 3² (∵ 3^2x ≠ -3) ⇒ 2x = 2 ⇒ x = 1.