• Matéria: Matemática
  • Autor: Juliinhaa
  • Perguntado 9 anos atrás

Resolva as esquaçoes

A) log (3x-1) + log x=2
√2 √2

B) log (x2 - 3 ) = 0
10

Respostas

respondido por: korvo
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\}}
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