Question

7(a-1)-2(a-5)=a-5
Essa é pra aquecer a cuca

Answer 1

$\text{Acompanhe.}$

$\displaystyle 7(a-1)-2(a-5)=a-5\\\\\text{Seja } a-5=\ln x.\text{ Ent\~ao,}\\\\7(a-5+4)=7(\ln x+4)=3(a-5)=3\ln x\\\\7(\ln x+4)=3\ln x\\\\7\ln x+28=3\ln x\\\\\ln x^7+\ln e^{28}=\ln x^3\\\\\ln x^7-\ln x^3=\ln e^{-28}\\\\\ln x^4=\ln e^{-28}\\\\x^4=e^{-28}\\\\x=\pm\sqrt[4]{e^{-28}}=\pm e^{-7}.\\\\ \text{Uma vez que }x>0,\text{ }x=e^{-7}=e^{-7+2\pi ki}.$

$\displaystyle \text{Assim,}\\\\a-5=\ln x.\\\\\text{Como queremos o valor principal} \in R,\\\\a-5=\text{Ln } e^{-7}\\\\a-5=\ln r+i\arg e^{-7+2\pi ki}\\\\a-5=\frac{1}{2}\ln(0^2+e^{-14})+i\text{Arg }e^{7-2\pi ki}\\\\a=5+\frac{1}{2}\ln e^{-14}+i\arctan\frac{0}{e^{-7+2\pi ki}}.\\\\\text{Assumindo }k=0,\\\\a=5-\frac{14}{2}+0i.\\\\a=-2.\\\\\text{Portanto,}\\\\a=-2$

$\text{Tem raz\~ao, essa \'e pra aquecer a cuca.}\\\\\text{Bons estudos, ma dear.}$