Bài toán: Giải các phương trình sau

1) ${\log _2}\frac{5}{x} = {\log _5}2x$

2) ${\log _2}2{x^2} + {\log _3}\frac{3}{x} + {\log _5}5\sqrt x = 3$

3) ${\log _{\frac{2}{x}}}4{x^3} + {\log _{2{x^2}}}\frac{2}{{\sqrt x }} = 3$

4) ${\log _2}\frac{1}{x}{\log _{\sqrt x }}{(x + 1)^2}{\log _{\frac{1}{{\sqrt {x + 1} }}}}4 = 16{\log _2}(x + 1)$

5) $x + {x^{{{\log }_2}3}} = 1 + {x^{(1 + {{\log }_2}3)}}$

6) ${\log _2}\left( {\frac{{{x^2} + 3}}{{2{x^2} + 1}}} \right) = {x^2} - 2$

7) ${\log _2}\frac{2}{x} + \left( {{{\log }_3}3x} \right)\left( {{{\log }_5}5x} \right) = \left( {{{\log }_3}3x + {{\log }_5}5x} \right){\log _2}\frac{2}{x}$.