Logarithm problems and solutions

$(1). \,\,\,$ Find the value of $\log_{21}{(x)}$ if $\log_{3}{(x)} = a$ and $\log_{7}{(x)} = b$

$(2). \,\,\,$ Find the angle satisfying the equation $4\log_{16}{(\cos{2x})}$ $+$ $2\log_{4}{(\sin{x})}$ $+$ $\log_{2}{(\cos{x})}$ $+3$ $\,=\,$ $0$