log2 2 x + 2 log2 x + 1 = 0 lg2 x - 5lg x + 6 = 0log6 2 x + log6 x6 + 5 = 0

1)

$\displaystyle log^2_2x+2log_2x+1=0\\\\ODZ: x\ \textgreater \ 0\\\\log_2x=t\\\\t^2+2t+1=0\\\\(t+1)^2=0\\\\t=-1\\\\Log_2x=-1\\\\x=2^{-1}= \frac{1}{2}$

2)

$\displaystyle lg^2x-5lgx+6=0\\\\ODZ:x\ \textgreater \ 0\\\\lgx=t\\\\t^2-5t+6=0\\\\D=25-24=1\\\\t_{1.2}= \frac{5\pm 1}{2}; t_1=3; t_2=2\\\\lgx=3; x=10^3; x=1000\\\\lgx=2; x=10^2; x=100$

3)

$\displaystyle log_6^2x+log_6x^6+5=0\\\\ODZ:x\ \textgreater \ 0\\\\log_6^2x+6log_6x+5=0\\\\log_6x=t\\\\t^2+6t+5=0\\\\D=36-20=16=4^2\\\\t_{1.2}= \frac{-6\pm 4}{2}; t_1=-5; t_2=-1\\\\log_6x=-5; x=6^{-5}; x= \frac{1}{6^5}\\\\log_6x=-1; x=6^{-1}; x= \frac{1}{6}$