Question

resolva a seguinte equação exponencial na variável x


$({10}^{x} ) {}^{1 - x} = 0.000001$
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Answer 1

Resposta:

x= -2 ou x=3

Explicação passo-a-passo:

$\displaystyle\\(10^{x})^{1-x}=0,000001\\\\10^{x(1-x)}=10^{-6}\\\\x(1-x)=-6\\x-x^{2}=-6\\-x^{2}+x+6=0\\\\Aplicando~a~f\'{o}rmula~de~Bhaskara~para~-1x^{2}+1x+6=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=-1{;}~b=1~e~c=6\\\\\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(-1)(6)=1-(-24)=25\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(1)-\sqrt{25}}{2(-1)}=\frac{-1-5}{-2}=\frac{-6}{-2}=3\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(1)+\sqrt{25}}{2(-1)}=\frac{-1+5}{-2}=\frac{4}{-2}=-2$