Question

2log7(x)=log7(3x)+log7(6)

Answer 1

$\mathrm{2\log_7{x}=\log_7{3x}+\log_7{6}}\\ \mathrm{\log_7{x^2}=\log_7{(3x.6)}\ \to\ \log_7{x^2}=\log_7{18x}}\\\\ \mathrm{x^2=18x\ \to\ x^2-18x=0\ \to\ x(x-18)=0}\\ \mathrm{x=0\ \to\ \nexists\log{x}\ \ \|\ \ x-18=0\ \to\ x=18\ \to\ \exists\log{x}}\\\\ \mathbf{S=\{18\}}$