设t=lgx，则lg²x-lgx²-2=0可化为t²-2t-2=0
∵△＞0∴t₁+t₂=2，t₁×t₂=-2
∴lgα+lgβ=2，lgα×lgβ=-2
∵log_αβ+log_βα=

lgβ

lgα

+

lgα

lgβ

=

lg2β+lg2α

lgα•lgβ

=

(lg β+lg α)

lgα•lgβ

=

(lgα+lgβ)2−2lgα•lgβ

lgα•lgβ

=

22−2×(−2)

−2

=-4
故填-4