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