Question

sendo log a(base x)=6 log b(base x)=4 e log c(base x)=2? me ajudeeem por favor!

Answer 1

$log_xa=6 ==\ \textgreater \ x^6=a (eq1) \\ log_xb=4 ==\ \textgreater \ x^4=b (eq2) \\ Da\, \, (eq1){:}\ \\ a=x^{6} = x^4.x^2 \\ \\ Substituindo\,\, x^4=b\,\, (eq2) \\ \\ a= x^4.x^2 =b.x^2 \Rightarrow x^2= \frac{a}{b} \,\,(eq3)\\ \\ log_xc=2 ==\ \textgreater \ x^2=c \\ \\ Substituindo\,\, x^2= \frac{a}{b} \,\, (eq3) \\ \\ \frac{a}{b} =c\\ \\ a=b.c \\ \\ \boxed{Resposta{:}\ a=b.c }$