Question Number 109817 by Algoritm last updated on 25/Aug/20
Commented by 1549442205PVT last updated on 26/Aug/20
![This question is repeated question Q109721.Here,you wrote the question in an ambiguous way I solve it in the case log_3 [(6−x)(√(x^2 +2x+6))]=x If it is [log_3 (6−x)](√(x^2 +2x+6))]=x then then the equation has unique root x≈3.8.The proof is similar to the above case](https://www.tinkutara.com/question/Q110007.png)
$$\mathrm{This}\:\mathrm{question}\:\mathrm{is}\:\mathrm{repeated}\:\mathrm{question} \\ $$$$\mathrm{Q109721}.\mathrm{Here},\mathrm{you}\:\mathrm{wrote}\:\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{ambiguous}\:\mathrm{way} \\ $$$$\mathrm{I}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{in}\:\mathrm{the}\:\mathrm{case}\:\mathrm{log}_{\mathrm{3}} \left[\left(\mathrm{6}−\mathrm{x}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{6}}\right]=\mathrm{x} \\ $$$$\left.\mathrm{If}\:\mathrm{it}\:\mathrm{is}\:\left[\mathrm{log}_{\mathrm{3}} \left(\mathrm{6}−\mathrm{x}\right)\right]\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{6}}\right]=\mathrm{x}\:\mathrm{then} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{unique}\:\mathrm{root} \\ $$$$\mathrm{x}\approx\mathrm{3}.\mathrm{8}.\mathrm{The}\:\mathrm{proof}\:\mathrm{is}\:\mathrm{similar}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{above}\:\mathrm{case} \\ $$