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Question-141104




Question Number 141104 by Opredador last updated on 15/May/21
Answered by hknkrc46 last updated on 15/May/21
 {: (((√7^(√(63)) ) = (√7^(3(√7)) ) = 7^(√7) (√7^(√7) ))),((7^(√7)  = u)) } ((u(√u) − (√u))/(u − 1))  = (((√u)(u − 1))/(u − 1)) = (√u) = (√7^(√7) )
$$\left.\begin{matrix}{\sqrt{\mathrm{7}^{\sqrt{\mathrm{63}}} }\:=\:\sqrt{\mathrm{7}^{\mathrm{3}\sqrt{\mathrm{7}}} }\:=\:\mathrm{7}^{\sqrt{\mathrm{7}}} \sqrt{\mathrm{7}^{\sqrt{\mathrm{7}}} }}\\{\mathrm{7}^{\sqrt{\mathrm{7}}} \:=\:\boldsymbol{{u}}}\end{matrix}\right\}\:\frac{\boldsymbol{{u}}\sqrt{\boldsymbol{{u}}}\:−\:\sqrt{\boldsymbol{{u}}}}{\boldsymbol{{u}}\:−\:\mathrm{1}} \\ $$$$=\:\frac{\sqrt{\boldsymbol{{u}}}\left(\boldsymbol{{u}}\:−\:\mathrm{1}\right)}{\boldsymbol{{u}}\:−\:\mathrm{1}}\:=\:\sqrt{\boldsymbol{{u}}}\:=\:\sqrt{\mathrm{7}^{\sqrt{\mathrm{7}}} } \\ $$

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