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

$$\mathbf{solve}\mathbf{for}\mathbf{x}$$$${\mathbf{x}}^{{\mathbf{x}}^{\mathbf{x}}}=36$$$$$$

Commented by Frix last updated on 25/Nov/22

$$\mathrm{Approximation}\mathrm{gives}x\approx 2.10703646396$$

Commented by Frix last updated on 25/Nov/22

$${\mathrm{There}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{exact}\mathrm{solution}.$$

Commented by Socracious last updated on 25/Nov/22

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

Answered by yogamulyadi last updated on 25/Nov/22

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

Commented by Frix last updated on 25/Nov/22

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

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