Find the values of parameter $a$ so that....

Question

Determine all the values of real parameter $a$ so that the equation:$$(x-a)[log_4(x-5)-1]=0$$ admits a maximum number of real solutions. Thank you!

Answer 1

$$(x-a)(\log_4(x-5)-1)=0\\(x-a)=0\lor \log_4(x-5)=1\\x=a\lor x=9$$ Now if $a\not= 9$ then solutions are $x_1=a,x_2=9$,so maximum number of solutions is for $a\not=9$