Question Number 39689 by Cheyboy last updated on 09/Jul/18
$${In}\:{Lambert}\:{W}\:{Function} \\ $$$$ \\ $$$${How}\:{would}\:{i}\:{simplify} \\ $$$$ \\ $$$${x}\:=\:−\:\frac{{W}\left(\frac{−{ln}\left(\mathrm{4}\right)}{\mathrm{8}}\right)}{{ln}\left(\mathrm{4}\right)} \\ $$$${To}\:{get}\:{the}\:{values} \\ $$$$ \\ $$
Commented by MrW3 last updated on 09/Jul/18
$${You}\:{can}\:{not}\:{really}\:{simplify}\:{further}. \\ $$$${Certainly}\:{you}\:{can}\:{write} \\ $$$${x}\:=\:−\:\frac{{W}\left(\frac{−{ln}\left(\mathrm{2}\right)}{\mathrm{4}}\right)}{\mathrm{2}\:{ln}\left(\mathrm{2}\right)} \\ $$$${but}\:{this}\:{doesn}'{t}\:{really}\:{help}\:{you}. \\ $$$${To}\:{get}\:{the}\:{values}\:{of}\:{x},\:{you}\:{just}\:{need} \\ $$$${to}\:{determine}\:{W}\left(−\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}}\right)\:{which}\:{is} \\ $$$$−\mathrm{0}.\mathrm{2148}\:{or}\:−\mathrm{2}.\mathrm{7726}.\: \\ $$$$\Rightarrow{x}=−\frac{−\mathrm{0}.\mathrm{2148}}{\mathrm{2}\:\mathrm{ln}\:\mathrm{2}}=\mathrm{0}.\mathrm{1549}\:{or} \\ $$$$\Rightarrow{x}=−\frac{−\mathrm{2}.\mathrm{7726}}{\mathrm{2}\:\mathrm{ln}\:\mathrm{2}}=\mathrm{2} \\ $$$${If}\:{you}\:{have}\:{luck},\:{you}\:{may}\:{find}\:{an} \\ $$$${online}\:{calculator}\:{for}\:{Lambert}\:{function}. \\ $$
Commented by Cheyboy last updated on 09/Jul/18
$${Thank}\:{you}\:{sir},\:{I}\:{though}\:{their}\:{is} \\ $$$${a}\:{way}\:{to}\:{simplify}\:{further}.. \\ $$$${I}\:{will}\:{try}\:{an}\:{see}\:{whether}\:{i}\:{can} \\ $$$${access}\:{it} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Answered by Cheyboy last updated on 09/Jul/18
$${Sir}\:{W}\mathrm{3}\:{ur}\:{help}\:{is}\:{needed}\:{cuz}\:{you} \\ $$$${usually}\:{attept}\:{related}\:{question} \\ $$