Question Number 45500 by Sanjarbek last updated on 13/Oct/18
Answered by MrW3 last updated on 13/Oct/18
$${x}=\mathrm{64}^{\frac{\mathrm{1}}{{x}}} ={e}^{\frac{\mathrm{ln}\:\mathrm{64}}{{x}}} \\ $$$$\mathrm{1}=\frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{64}}{{x}}} \\ $$$$\mathrm{ln}\:\mathrm{64}=\frac{\mathrm{ln}\:\mathrm{64}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{64}}{{x}}} \\ $$$$\frac{\mathrm{ln}\:\mathrm{64}}{{x}}=\mathbb{W}\left(\mathrm{ln}\:\mathrm{64}\right)\:\leftarrow{Lambert}\:{W}\:{function} \\ $$$$\Rightarrow{x}=\frac{\mathrm{ln}\:\mathrm{64}}{\mathbb{W}\left(\mathrm{ln}\:\mathrm{64}\right)}=\frac{\mathrm{ln}\:\mathrm{64}}{\mathrm{1}.\mathrm{223517}}=\mathrm{3}.\mathrm{3991} \\ $$
Commented by Cheyboy last updated on 14/Oct/18
$$\mathrm{Sir}\:\mathrm{Mr}\:\mathrm{W}_{\mathrm{3}} \:\mathrm{how}\:\mathrm{can}\:\mathrm{i}\:\mathrm{have}\:\mathrm{acess} \\ $$$$\mathrm{to}\:\mathrm{Lambert}\:\mathrm{function}\:\mathrm{calculator} \\ $$
Commented by Joel578 last updated on 14/Oct/18
$$\mathrm{wolframalpha}.\mathrm{com} \\ $$
Commented by Cheyboy last updated on 14/Oct/18
$$\mathrm{Ok}\:\mathrm{thank}\:\mathrm{u}\:\mathrm{sir} \\ $$