## Solve the equation for n

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### Solution

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\begin{aligned} &\left(n^{2}\right)^{n}-2 n^{n}+1=0 \\\\ &\left(n^{n}\right)^{2}-2 n^{n}+1=0 \\\\ &\operatorname{Let} x=n^{n}, \\\\ &x^{2}-2 x+1=0 \\\\ &(x-1)^{2}=0 \\\\ &x=1 \Rightarrow n^{n}=1 \\\\ &\operatorname{ln}\left(n^{n}\right)=\operatorname{ln}(1) \\\\ &n \operatorname{ln} n=0 \\\\ &n \neq 0 \text { thus } \operatorname{ln} n=0 \\\\ &\Rightarrow n=1 \end{aligned}
Home -> Solved problems -> Solve the equation for n

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Solve the equation for n
Home -> Solved problems -> Solve the equation for n