Question

find the value of x

${2}^{2x} - {2}^{x + 3} + {2}^{4} = 0$
solve fast urgent

Answer 1

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Answer 2

$Given : 2^{2x} - 2^{x + 3} + 2^4 = 0$

⇒ (2^x)^2 - (2)^x * (2)^3 + (2)^4 = 0

Let 2^x = a

⇒ a^2 - a * 8 + 16 = 0

⇒ a^2 - 8a + 16 = 0

⇒ a^2 - 4a - 4a + 16 = 0

⇒ a(a - 4) - 4(a - 4) = 0

⇒ (a - 4)(a - 4) = 0

⇒ (a - 4)^2 = 0

⇒ a = 4.

Then, 2^x = 4

⇒ 2^x = 2^2

⇒ x = 2.

Therefore, the value of x = 2.

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