Question

Qual o conjunto solução da equação log2 ( x2 - 9X + 18 ) = log2 ( x2 - 8x + 7 ) .

Answer 1

Lembrando que sendo 0 < a ≠ 1

$\fbox{ \ell og_a~f(x)=\ell og_a~g(x)~\Longleftrightarrow~f(x)=g(x)~~\ \textgreater \ 0 }$

Sendo assim

$\ell og_2(x^2-9x+18)=\ell og_2(x^2-8x+7)\\\\x^2{\hspace{-10}\diagup}-9x+18=x^2{\hspace{-10}\diagup}-8x+7~~~~\ \textgreater \ 0\\\\-9x+18=-8x+7~~~~\\\\-9x+18+8x-7=0\\\\-9x+8x+18-7=0\\\\-x+11=0\\\\x=11\\\\\\S=\begin{Bmatrix}11\end{Bmatrix}~~\leftarrow~conjunto~solu\c{c}\~ao$