The logarithmic equations are formed by the logarithmic terms and the trigonometric equations are formed by the trigonometric functions. Similarly, the both logarithmic and trigonometric functions form special equations in which logarithmic and trigonometric functions are involved. Here is the list of logarithmic trigonometric equations to solve.

$(1) \,\,\,$ Solve $4\log_{16}{(\cos{2x})}$ $+$ $2\log_{4}{(\sin{x})}$ $+$ $\log_{2}{(\cos{x})}$ $+$ $3$ $\,=\,$ $0$

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