Question

Resolver: (Lnx)^2-Ln(1/x)=6

Answer 1

$(lnx)^2-ln(\frac{1}{x})=6 \\ \\ (lnx)^2-(-lnx)=6 \\ \\ (lnx)^2+lnx-6=0 \\ \\ \boxed{lnx=y} \\ \\ y^2+y-6=0 \\ \\ S=\{ -3;2 \} \\ \\ lnx=-3 \rightarrow x=\frac{1}{e^3} \\ \\ lnx=2 \rightarrow x =e^2$