Question

log4 (x-2)+log1/2 (x-2)=1/2

Answer 1

$log_4 (x-2)+log_frac{1}{2} (x-2)=frac{1}{2}\ log_{2^2} (x-2)+log_{2^{-1}} (x-2)=frac{1}{2}\ 2log_{2} (x-2)-log_{2} (x-2)=frac{1}{2}\\ log_{2} (x-2)^2-log_{2} (x-2)=frac{1}{2}*log_2(2)\ log_2 (frac{(x-2)^2}{x-2} )=log_2( sqrt{2} )\\ left { {{frac{(x-2)^2}{x-2}= sqrt{2} } atop {x-2 textgreater 0}} right. \ left { {{x-2= sqrt{2} } atop {x textgreater 2}} right. \ x=2+ sqrt{2}$