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