Question

Determine, em função de A, B e C, o valor de x na equação: log(x)2 + 2.log(A)2 - Colog(B)2 - 4.log(C)2 = 3

Obs: É Log de x na base 2, mesma coisa com os outros.

Answer 1

$log_2(x)+2log_2(a)-colog_2(b)-4log_2(c)=3\\\\ log_2(x)+2log_2(a)-(colog_2(b)+4log_2(c))=3\\\\ log_2(x)+log_2(a^2)-(log_2(b^{-1})+log_2(c^4))=3\\\\ log_2(a^2\times x)-(log_2(b^{-1}\times c^4))=3\\\\ log_2(\frac{a^2\times x}{b^{-1}\times c^4})= 3\\\\ 2^3=\frac{a^2\times x}{b^{-1}\times c^4}\\\\ 8\times b^{-1}\times c^4=a^2\times x\\\\ x=\frac{8\times b^{-1}\times c^4}{a^2}\\\\ x=\frac{8\times \frac{1}{b} \times c^4}{a^2}\\\\ x=\frac{\frac{8\times c^4}{b}}{a^2}\\\\ \boxed{x=\frac{8\times c^4}{b\times a^2}}$