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$\Huge \color{#3D99F6}{2}^{\color{#D61F06}{16}^{\color{#20A900}{x}}} = \color{#D61F06}{16}^{\color{#3D99F6}{2}^{\color{#20A900}{x}}}$

Solve the above equation for $x.$ Give your answer to 3 decimal places.

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