Question

se log x + log x^3 + log x^4 = -20, o valor de x é:
a) 10
b)0,1
c)100
d)0,01
e)1

Answer 1

$log(x)+log(x^3)+log(x^4)=-20\\ \\ log(x)+3log(x)+4log(x)=-20\\ \\ 8log(x)=-20\\ \\ logx=-\frac{20}{8}=-\frac{5}{2}\\ \\ x=10^{-\frac{5}{2}}\approx 0,0031$

Answer 2

$\text{log}(x)+\text{log}(x^3)+\text{log}(x^4)=-20$

Veja que:

$\text{log}(x^3)=3\text{log}(x)$

$\text{log}(x^4)=4\text{log}(x)$

Assim:

$\text{log}(x)+3\text{log}(x)+4\text{log}(x)=-20$

$8\text{log}(x)=-20$

$\text{log}(x)=\dfrac{-20}{8}$

$\text{log}(x)=\dfrac{-5}{2}$

Logo, $x=10^{\frac{-5}{2}}\approx0,00316$