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Givne that: $$2^{x}=3^{\log_{5}{2}}$$
$$\Rightarrow$$ $$2^{x}=2^{\log_{5}{3}}$$
$$\Rightarrow$$ $$x=\log_{5}{3}$$
$$\Rightarrow$$ $$x=\log_{5}{\dfrac{3*5}{5}}$$
$$\Rightarrow$$ $$x=\log_{5}{5}+\log_{5}{\dfrac{3}{5}}$$
$$\Rightarrow$$ $$x=1+\log_{5}{\dfrac{3}{5}}$$. Hence, option D is the correct answer.
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