The equation [math] \log_2 {2 \cdot x^2} + \log_2 x \cdot x^{\log {\log x + 1}} + \dfrac{1}{2} \cdot \log^2_4 x^4 + 2^{-3 \cdot \log_\dfrac {3}{2} {\log x} [/math] has how many solutions?
valid question