Menu Close

2-x-x-x-2-2-x-




Question Number 192171 by mathlove last updated on 10/May/23
2^x^x^x   =2^(√2)   x=?
$$\mathrm{2}^{{x}^{{x}^{{x}} } } =\mathrm{2}^{\sqrt{\mathrm{2}}} \\ $$$${x}=? \\ $$
Commented by Frix last updated on 11/May/23
2^x^x^x   =2^((x^((x^x )) ))   ln 2^x^x^x    =ln 2^(√2)   x^x^x  =(√2)  x^x ln x =((ln 2)/2)  We can only approximate
$$\mathrm{2}^{{x}^{{x}^{{x}} } } =\mathrm{2}^{\left({x}^{\left({x}^{{x}} \right)} \right)} \\ $$$$\mathrm{ln}\:\mathrm{2}^{{x}^{{x}^{{x}} } } \:=\mathrm{ln}\:\mathrm{2}^{\sqrt{\mathrm{2}}} \\ $$$${x}^{{x}^{{x}} } =\sqrt{\mathrm{2}} \\ $$$${x}^{{x}} \mathrm{ln}\:{x}\:=\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{2}} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$
Commented by mathlove last updated on 11/May/23
ok
$${ok} \\ $$
Answered by josemate19 last updated on 10/May/23
ln2x^x^x  =ln2^(√2)   x^x ln2x=(√2)ln2  x^x =(((√2)ln2)/(ln2x))  lnx^x =ln((((√2)ln2)/(ln2x)))    xlnx=ln((((√2)ln2)/(ln2x)))    x=((ln((((√2)ln2)/(ln2x))))/(lnx))    x=((ln(((ln2^(√2) )/(ln2x))))/(lnx))
$${ln}\mathrm{2}{x}^{{x}^{{x}} } ={ln}\mathrm{2}^{\sqrt{\mathrm{2}}} \\ $$$${x}^{{x}} {ln}\mathrm{2}{x}=\sqrt{\mathrm{2}}{ln}\mathrm{2} \\ $$$${x}^{{x}} =\frac{\sqrt{\mathrm{2}}{ln}\mathrm{2}}{{ln}\mathrm{2}{x}} \\ $$$${lnx}^{{x}} ={ln}\left(\frac{\sqrt{\mathrm{2}}{ln}\mathrm{2}}{{ln}\mathrm{2}{x}}\right) \\ $$$$ \\ $$$${xlnx}={ln}\left(\frac{\sqrt{\mathrm{2}}{ln}\mathrm{2}}{{ln}\mathrm{2}{x}}\right) \\ $$$$ \\ $$$${x}=\frac{{ln}\left(\frac{\sqrt{\mathrm{2}}{ln}\mathrm{2}}{{ln}\mathrm{2}{x}}\right)}{{lnx}} \\ $$$$ \\ $$$${x}=\frac{{ln}\left(\frac{{ln}\mathrm{2}^{\sqrt{\mathrm{2}}} }{{ln}\mathrm{2}{x}}\right)}{{lnx}} \\ $$
Commented by Frix last updated on 11/May/23
Wrong.
$$\mathrm{Wrong}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *