Question

$(3 + 2 \sqrt{2} ) {}^{x} = (1 + \sqrt{2} ) {}^{2}$
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Answer 1

$(3+2\sqrt 2)^x = (1+\sqrt 2)^2 \\ \\ \Big[(1+\sqrt 2)^2\Big]^x = (1+\sqrt 2)^2 \\ \\ (1+\sqrt 2)^{2x} = (1+\sqrt 2)^2\\ \\ 2x = 2 \Rightarrow \boxed{x = 1}$