Question

Resolvendo a equação log2 (x^2 - 2x +1) = 2, encontramos o conjunto solução:

Answer 1

Pela definição: 

$\large\fbox{ \ell og_a(b)=y~\Longleftrightarrow~a^y=b~~~~(0\ \textless \ a\neq1) }$

Sendo assim...

$\large\begin{array}{l}\ell og_2(x^2-2x+1)=2~\Longleftrightarrow~2^2=x^2-2x+1\\\\x^2-2x+1=4\\\\(x-1)^2=4\\\\\sqrt{(x-1)^2}=\sqrt{4}\\\\|x-1|=2\\\\x-1=\pm~2\\\\\\\begin{Bmatrix}x=-2+1~\Rightarrow~x=-1\\\\ou\\\\x=2+1~\Rightarrow~x=3~~~~~\end.\\\\\\\fbox{ S=\begin{Bmatrix}x=-1~~ou~~x=3\end{Bmatrix} }~~\leftarrow\text{conjunto~solu\c{c}\~ao!}\end{array}$