The roots of the equation 4^x - 3 cdot 2^{x+2 | vedclass

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(D) Given equation is: $4^x - 3 \cdot 2^{x+2} + 32 = 0$Since $4^x = (2^2)^x = (2^x)^2$ and $2^{x+2} = 2^x \cdot 2^2 = 4 \cdot 2^x$,the equation become

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$2$ and $3$

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(D) Given equation is: $4^x - 3 \cdot 2^{x+2} + 32 = 0$Since $4^x = (2^2)^x = (2^x)^2$ and $2^{x+2} = 2^x \cdot 2^2 = 4 \cdot 2^x$,the equation becomes:$(2^x)^2 - 3 \cdot (4 \cdot 2^x) + 32 = 0$$(2^x)^2 - 12 \cdot 2^x + 32 = 0$Let $2^x = y$. Then the equation is $y^2 - 12y + 32 = 0$.Factoring the quadratic equation: $(y - 8)(y - 4) = 0$.So,$y = 8$ or $y = 4$.Substituting $y = 2^x$ back:$2^x = 8 \Rightarrow 2^x = 2^3 \Rightarrow x = 3$$2^x = 4 \Rightarrow 2^x = 2^2 \Rightarrow x = 2$Thus,the roots are $2$ and $3$.

The roots of the equation $4^x - 3 \cdot 2^{x+2} + 32 = 0$ are

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