Question

please find the value of x​

Answer 1

Answer:

x = 2

Step-by-step explanation:

[ Refer to the attachment ]

• Quadratic solved by splitting the middle term

• when base is equal exponents are equal !

${a}^{m} = {a}^{n} \\ m = n$

Answer 2

$\large \bf \orange{SOLUTION : }$

$\bf \Longrightarrow{2}^{2x} - {2}^{x + 3} + {2}^{4} = 0 \\ \\ \bf \Longrightarrow {2}^{x} \times {2}^{x} - {2}^{x} \times {2}^{3} + {2}^{4} = 0 \\ \\ \bf let \: {2}^{x} = y \\ \\ \bf \Longrightarrow{y}^{2} - 8y + 16 = 0 \\ \\ \bf \Longrightarrow{y}^{2} - 4y - 4y + 16 = 0 \\ \\ \bf \Longrightarrow y(y - 4) - 4(y - 4) = 0 \\ \\ \bf \Longrightarrow (y - 4)(y - 4) = 0 \\ \\ \bf \Longrightarrow y = 4$

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$\bf {2}^{x} = y \\ \\ \bf y = 4 = {2}^{2} \\ \\ \bf{2}^{x} = {2}^{2} \\ \\ \large \underline{\boxed{ \bf \green{x = 2}}}$