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Question Number 172078 by Mikenice last updated on 23/Jun/22

solve  ((2logx)/(log(5x−4)))=1

$${solve} \\ $$$$\frac{\mathrm{2}{logx}}{{log}\left(\mathrm{5}{x}−\mathrm{4}\right)}=\mathrm{1} \\ $$

Answered by Rasheed.Sindhi last updated on 23/Jun/22

((2logx)/(log(5x−4)))=1  2logx=log(5x−4)  logx^2 =log(5x−4)  x^2 =5x−4  x^2 −5x+4=0  (x−1)(x−4)=0  x=1, 4

$$\frac{\mathrm{2}{logx}}{{log}\left(\mathrm{5}{x}−\mathrm{4}\right)}=\mathrm{1} \\ $$$$\mathrm{2}{logx}={log}\left(\mathrm{5}{x}−\mathrm{4}\right) \\ $$$${logx}^{\mathrm{2}} ={log}\left(\mathrm{5}{x}−\mathrm{4}\right) \\ $$$${x}^{\mathrm{2}} =\mathrm{5}{x}−\mathrm{4} \\ $$$${x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}=\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)=\mathrm{0} \\ $$$${x}=\mathrm{1},\:\mathrm{4} \\ $$

Commented by kaivan.ahmadi last updated on 23/Jun/22

x=1 is not answer since  log(5x−4)∣_(x=1) =0

$${x}=\mathrm{1}\:{is}\:{not}\:{answer}\:{since} \\ $$$${log}\left(\mathrm{5}{x}−\mathrm{4}\right)\mid_{{x}=\mathrm{1}} =\mathrm{0} \\ $$$$ \\ $$

Commented by Rasheed.Sindhi last updated on 23/Jun/22

Right sir!

$$\mathcal{R}{ight}\:\boldsymbol{{sir}}! \\ $$

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