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Answer it with steps...

Find the value of x
${2}^{2x} - {2}^{x + 3} + {2}^{4} = 0$

Answer 1

$4x - 2x + 3 + 8 = 0 \\ 2x + 3 + 8 = 0 \\ 2x + 11 = 0 \\ 2x = 0 - 11 \\ 2x = 1 \\ x = 1$
2×2

Answer 2

Answer:

x = 2

Step-by-step explanation:

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

$=>(2^x)^2 - 2^x * 2^3 + 2^4 = 0$

Let u = 2^x

$=> (u)^2 - u * 2^3 + 2^4 = 0$

$=>u^2 - 8u + 16 = 0$

$=>u^2 - 4u - 4u + 16 = 0$

$=>u(u - 4) - 4(u - 4) = 0$

$=>(u - 4)(u - 4) = 0$

$=>(u - 4)^2 = 0$

$=>u = 4$

Now,

$=>2^x = 4$

$=>2^x = 2^2$

$=>x = 2$

Hope it helps!