如果\(x\)满足方程\(\log{x} = \log{322} - \frac{\log{49}}{2}\),那么\(x\)的值是多少?
假设\(0 \leq x \leq \pi \)满足\[\log_{\ sinx}{\cos x} + \log_{\cos x}{\ tanx} = 1。如果(x = \frac{a}{b}\pi\),其中\(a\)和\(b\)是互素正整数,那么\(a+b\)的值是多少?
\(x\)和\(y\)是实数,满足以下两个方程:\[3^x \cdot 2^y = 3456 \;\;\;\ textrm{和}\;\ \;\log_{\根号{2}}(y-x) = 4;(x + y)的值是多少?
\(x)满足\[3 \log_x 2 + \log_{2} x = 4的所有实值之和是多少?\]