Question Number 199836 by Calculusboy last updated on 10/Nov/23
Commented by Rasheed.Sindhi last updated on 10/Nov/23
$$\mathcal{D}{o}\:{you}\:{mean}\:\mathrm{2}^{{x}^{\mathrm{2}} } =\mathrm{16}\:? \\ $$$${If}\:{so}: \\ $$$$\mathrm{2}^{{x}^{\mathrm{2}} } =\mathrm{2}^{\mathrm{4}} \\ $$$${x}^{\mathrm{2}} =\mathrm{4} \\ $$$${x}=\pm\mathrm{2} \\ $$
Commented by AST last updated on 10/Nov/23
$${Tetration}:\:^{\mathrm{2}} {x}={x}^{{x}} ;^{\mathrm{3}} \mathrm{2}=\mathrm{2}^{\mathrm{2}^{\mathrm{2}} } \\ $$$$\mathrm{16}=\mathrm{2}^{\mathrm{2}^{\mathrm{2}} } =^{\mathrm{3}} \mathrm{2}=^{\:^{\mathrm{2}} {x}} \mathrm{2}\Rightarrow^{\mathrm{2}} {x}=\mathrm{3}\Rightarrow{x}^{{x}} =\mathrm{3}\Rightarrow{x}\approx\mathrm{1}.\mathrm{825455} \\ $$
Commented by Rasheed.Sindhi last updated on 10/Nov/23
$$\mathcal{T}{hank}\:{you}\:{sir}! \\ $$