Question

Resolva as esquaçoes

A) log (3x-1) + log x=2
√2 √2

B) log (x2 - 3 ) = 0
10

Answer 1

$\log_{ \sqrt{2}}(3x-1)+\log_{ \sqrt{2}}(x)=2\\ \log_{ \sqrt{2}}[x\cdot(3x-1)]=2\\ \log_{ \sqrt{2}}(3x^2-x)=2\\ 3x^2-x=( \sqrt{2})^2\\ 3x^2-x=2\\ 3x^2-x-2=0~~(eq.~do~2^o~grau)\\\\ x_1=- \dfrac{2}{3}~~(\notin~\mathbb{R})~~e~~x_2=1\\\\ \boxed{S=\{1\} }$

$\log_{10}(x^2-3)=0\\ \log_{10}(x^2-3)=\log_{10}(1)\\\\ x^2-3=1\\ x^2=4\\ x=\pm \sqrt{4}\\\\ x=\pm2\\\\ \boxed{S=\{2,-2\}}$