Menu Close

x-x-x-3-x-




Question Number 103170 by shaxzod last updated on 13/Jul/20
x^x^x  =3      x=?
$${x}^{{x}^{{x}} } =\mathrm{3}\:\:\:\:\:\:{x}=? \\ $$$$ \\ $$
Commented by mr W last updated on 13/Jul/20
x≈1.6351  no formula, no exact solution  possible!
$${x}\approx\mathrm{1}.\mathrm{6351} \\ $$$${no}\:{formula},\:{no}\:{exact}\:{solution} \\ $$$${possible}! \\ $$
Commented by Dwaipayan Shikari last updated on 13/Jul/20
If it is x^x =3  then solution will be  xlogx=log3  logxe^(logx) =log3  logx=W_0 (log3)  x=e^(W_0 (log3))   x=1.8235..  But now it is hard to solve x^x^x  =3  Using calculator it is solveable
$${If}\:{it}\:{is}\:{x}^{{x}} =\mathrm{3} \\ $$$${then}\:{solution}\:{will}\:{be} \\ $$$${xlogx}={log}\mathrm{3} \\ $$$${logxe}^{{logx}} ={log}\mathrm{3} \\ $$$${logx}={W}_{\mathrm{0}} \left({log}\mathrm{3}\right) \\ $$$${x}={e}^{{W}_{\mathrm{0}} \left({log}\mathrm{3}\right)} \\ $$$${x}=\mathrm{1}.\mathrm{8235}.. \\ $$$${But}\:{now}\:{it}\:{is}\:{hard}\:{to}\:{solve}\:{x}^{{x}^{{x}} } =\mathrm{3} \\ $$$${Using}\:{calculator}\:{it}\:{is}\:{solveable} \\ $$
Commented by shaxzod last updated on 13/Jul/20
which calculator can solve it?
$${which}\:{calculator}\:{can}\:{solve}\:{it}? \\ $$

Leave a Reply

Your email address will not be published.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