Найдите значение выражения (1 - log₅40)(1 - log₈40).

(1 - log₅40)(1 - log₈40) = (log₅5 - log₅40)(log₈8 - log₈40)

= log₅(5/40) · log₈(8/40) = log₅(1/8) · log₈(1/5)

= (-log₅8) · (-log₈5) = log₅8 · log₈5 = log₅8 · (1/log₅8) = 1