Question

Qual é a solução para a equação x2 + x log 5 - log 2 = 0?? gostaria de saber, por favor.

Answer 1

$x^2+x\log5-\log2=0$

$\Delta=(\log5)^2-4\cdot1\cdot(-\log2)=2\cdot\log5+4\cdot\log2=\log25+\log16=\log400$

$x=\dfrac{-\log5\pm\sqrt{\log400}}{2\cdot1}=\dfrac{-\log5\pm\log20}{2}$

$x'=\dfrac{-\log5+\log20}{2}=\dfrac{-\log5+\log4+\log5}{2}=\dfrac{2\log2}{2}=\log2$

$x"=\dfrac{-\log5-\log20}{2}=\dfrac{-\log5-\log4-\log5}{2}=-\log5-\log2$