Solve:
$3^{2 x + 4} + 1 = {2.3}^{x + 2}$

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Solution

$3^{2 x + 4} + 1 = 2 \cdot 3^{x + 2}$
$(3^{x + 2})^{2} + 1 = 2 \times 3^{x + 2}$
Let $A = 3^{x + 2}$
$\Rightarrow A^{2} + 1 = 2 A$
$\Rightarrow (A - 1)^{2} = 0$
$\Rightarrow A = 1$
$3^{(x + 2)} = 1$
$3^{(x + 2)} = 3^{0}$
$\Rightarrow x + 2 = 0$
$\Rightarrow x = - 2$

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