Question

Resolva a seguinte equação

logx−2 (2x – 4) = 2

Answer 1

$log_{x-2}(2x-4)=2 \\ (x-2)^{2}= 2x-4 \\ \\ x^{2}-4x+4 = 2x - 4 \\ \\ x^{2}-4x-2x+4+4 = 0 \\ \\ x^{2}-6x + 8 = 0 \\ \\ D = (-6)^{2}-4(1)(8) \\ \\ D = 36 - 32 = 4 \\ \\ \sqrt{D}= \sqrt{4}=2 \\ \\ x' = \frac{6 + 2}{2}= \frac{8}{2} = 4 \\ \\ x''= \frac{6 - 2}{2}= \frac{4}{2} = 2 \\ \\ CE: \\ 2x - 4 \ \textgreater \ 0 \\ 2x \ \textgreater \ 4 \\ x \ \textgreater \ \frac{4}{2} \\ x \ \textgreater \ 2 \\ \\ x - 2 \ \textgreater \ 0 =\ \textgreater \ x \ \textgreater \ 2\\ x - 2 \neq 1 =\ \textgreater \ x \neq 1 + 2 =\ \textgreater \ x \neq 3 \\ \\ Resposta: x = 4$


Espero ter ajudado.