Question Number 192851 by MATHEMATICSAM last updated on 29/May/23
$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{log}_{{a}^{\mathrm{2}} \sqrt{{x}}} \:{a}}{\mathrm{log}_{\mathrm{2}{x}} \:{a}}\:+\:\mathrm{log}_{{ax}} \:{a}\:.\:\mathrm{log}_{\frac{\mathrm{1}}{{a}}} \:\mathrm{2}{x}\:=\:\mathrm{0} \\ $$
Commented by Frix last updated on 29/May/23
$${x}=\frac{\mathrm{1}}{\mathrm{2}}\vee{x}={a}^{\mathrm{2}} \\ $$