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Question Number 181415 by Socracious last updated on 24/Nov/22

         solve  for x         x^x^x  =36

$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} } =\mathrm{36} \\ $$$$ \\ $$

Commented by Frix last updated on 25/Nov/22

Approximation gives x≈2.10703646396

$$\mathrm{Approximation}\:\mathrm{gives}\:{x}\approx\mathrm{2}.\mathrm{10703646396} \\ $$

Commented by Frix last updated on 25/Nov/22

There′s no exact solution.

$$\mathrm{There}'\mathrm{s}\:\mathrm{no}\:\mathrm{exact}\:\mathrm{solution}. \\ $$

Commented by Socracious last updated on 25/Nov/22

please show full solution

$$\mathrm{please}\:\mathrm{show}\:\mathrm{full}\:\mathrm{solution} \\ $$

Answered by yogamulyadi last updated on 25/Nov/22

x^x^x  =(6^n )^((2/2)(6^n )^((6^n )) )   x=6^n

$${x}^{{x}^{{x}} } =\left(\mathrm{6}^{{n}} \right)^{\frac{\mathrm{2}}{\mathrm{2}}\left(\mathrm{6}^{{n}} \right)^{\left(\mathrm{6}^{{n}} \right)} } \\ $$$${x}=\mathrm{6}^{{n}} \\ $$

Commented by Frix last updated on 25/Nov/22

Besides (2/2)=1 this makes no sense. you  could also claim x^x^x  =(17^n )^((17^n )^((17^n )) )  but this  is no solution.

$$\mathrm{Besides}\:\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1}\:\mathrm{this}\:\mathrm{makes}\:\mathrm{no}\:\mathrm{sense}.\:\mathrm{you} \\ $$$$\mathrm{could}\:\mathrm{also}\:\mathrm{claim}\:{x}^{{x}^{{x}} } =\left(\mathrm{17}^{{n}} \right)^{\left(\mathrm{17}^{{n}} \right)^{\left(\mathrm{17}^{{n}} \right)} } \:\mathrm{but}\:\mathrm{this} \\ $$$$\mathrm{is}\:\mathrm{no}\:\mathrm{solution}. \\ $$

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