Question Number 55458 by Gulay last updated on 24/Feb/19
Commented by Gulay last updated on 24/Feb/19
$$\mathrm{sir}\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 24/Feb/19
![2log_3 (x−4)^2 =xlog_3 (4−x) log_3 (x−4)^4 =log_3 (4−x)^x (x−4)^4 =(4−x)^x (4−x)^4 =(4−x)^x [since (x−4)^4 =(4−x)^4 ] 4=x x=4](https://www.tinkutara.com/question/Q55460.png)
$$\mathrm{2}{log}_{\mathrm{3}} \left({x}−\mathrm{4}\right)^{\mathrm{2}} ={xlog}_{\mathrm{3}} \left(\mathrm{4}−{x}\right) \\ $$$${log}_{\mathrm{3}} \left({x}−\mathrm{4}\right)^{\mathrm{4}} ={log}_{\mathrm{3}} \left(\mathrm{4}−{x}\right)^{{x}} \\ $$$$\left({x}−\mathrm{4}\right)^{\mathrm{4}} =\left(\mathrm{4}−{x}\right)^{{x}} \\ $$$$\left(\mathrm{4}−{x}\right)^{\mathrm{4}} =\left(\mathrm{4}−{x}\right)^{{x}} \:\left[{since}\:\left({x}−\mathrm{4}\right)^{\mathrm{4}} =\left(\mathrm{4}−{x}\right)^{\mathrm{4}} \right] \\ $$$$\mathrm{4}={x} \\ $$$${x}=\mathrm{4} \\ $$$$ \\ $$$$ \\ $$
Commented by Gulay last updated on 25/Feb/19
$$\mathrm{thanks}\:\mathrm{sir} \\ $$