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Question Number 55458 by Gulay last updated on 24/Feb/19

Commented by Gulay last updated on 24/Feb/19

sir plz help me

$$\mathrm{sir}\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

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

$$\mathrm{2}{log}_{\mathrm{3}} \left({x}−\mathrm{4}\right)^{\mathrm{2}} ={xlog}_{\mathrm{3}} \left(\mathrm{4}−{x}\right) \\ $$$${log}_{\mathrm{3}} \left({x}−\mathrm{4}\right)^{\mathrm{4}} ={log}_{\mathrm{3}} \left(\mathrm{4}−{x}\right)^{{x}} \\ $$$$\left({x}−\mathrm{4}\right)^{\mathrm{4}} =\left(\mathrm{4}−{x}\right)^{{x}} \\ $$$$\left(\mathrm{4}−{x}\right)^{\mathrm{4}} =\left(\mathrm{4}−{x}\right)^{{x}} \:\left[{since}\:\left({x}−\mathrm{4}\right)^{\mathrm{4}} =\left(\mathrm{4}−{x}\right)^{\mathrm{4}} \right] \\ $$$$\mathrm{4}={x} \\ $$$${x}=\mathrm{4} \\ $$$$ \\ $$$$ \\ $$

Commented by Gulay last updated on 25/Feb/19

thanks sir

$$\mathrm{thanks}\:\mathrm{sir} \\ $$

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