Question Number 172078 by Mikenice last updated on 23/Jun/22
$${solve} \\ $$$$\frac{\mathrm{2}{logx}}{{log}\left(\mathrm{5}{x}−\mathrm{4}\right)}=\mathrm{1} \\ $$
Answered by Rasheed.Sindhi last updated on 23/Jun/22
$$\frac{\mathrm{2}{logx}}{{log}\left(\mathrm{5}{x}−\mathrm{4}\right)}=\mathrm{1} \\ $$$$\mathrm{2}{logx}={log}\left(\mathrm{5}{x}−\mathrm{4}\right) \\ $$$${logx}^{\mathrm{2}} ={log}\left(\mathrm{5}{x}−\mathrm{4}\right) \\ $$$${x}^{\mathrm{2}} =\mathrm{5}{x}−\mathrm{4} \\ $$$${x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}=\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)=\mathrm{0} \\ $$$${x}=\mathrm{1},\:\mathrm{4} \\ $$
Commented by kaivan.ahmadi last updated on 23/Jun/22
$${x}=\mathrm{1}\:{is}\:{not}\:{answer}\:{since} \\ $$$${log}\left(\mathrm{5}{x}−\mathrm{4}\right)\mid_{{x}=\mathrm{1}} =\mathrm{0} \\ $$$$ \\ $$
Commented by Rasheed.Sindhi last updated on 23/Jun/22
$$\mathcal{R}{ight}\:\boldsymbol{{sir}}! \\ $$