Question

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

Answer 1

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) 

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

3) 

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