Question

Determine o conjunto dos valores reais x para que seja possivel definir:
a) log x(x-3)
b) log x(x-4)

Answer 1

$1 \neq \log_x(x-3)\ \textgreater \ 0\\ 1\neq x\ \textgreater \ 3\\ 1\neq x\ \textgreater \ 3\\\\ \Large\boxed{\text{S}=\{x\in\mathbb{R}~|~x\ \textgreater \ 3~~e~~x \neq 1\}}$



$\log_x(x^3-4)\\\\ x\ \textgreater \ 0~e~x \neq 1~(base)\\\\ x^3-4\ \textgreater \ 0\\ x^3\ \textgreater \ 4\\ x=\pm \sqrt[3]{4}\\\\ x_1=0~~(nao~covem)\\ x_2=4\\ x_3=-4~~(nao~convem)\\\\ \Large\boxed{\text{S}=\{x\in\mathbb{R}~|~x\ \textgreater \ 4~~e~~x \neq 1\}}$