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Question Number 160987 by cortano last updated on 10/Dec/21

$$\mathrm{Solve}\mathrm{for}\mathrm{x}$$$$\log {}_{\log {}_6(\mathrm{x}-1)}\left(64\right)=6$$

Answered by bobhans last updated on 10/Dec/21

$$\log {}_{\log {}_6(\mathrm{x}-1)}\left(64\right)=6$$$${\left[\log {}_6(\mathrm{x}-1)\right]}^6=64$$$$\log {}_6(\mathrm{x}-1)=\pm 2$$$$(\mathrm{x}-1)=\{\begin{array}{l}{6}^{-2}\\ 6^2\end{array}\Rightarrow \{\begin{array}{l}\mathrm{x}=1+\frac{1}{36}=\frac{37}{36}\\ \mathrm{x}=1+36=37\end{array}$$

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