Нужно доказать, log9 (6√6-15)^2+log27(6√6+15)^3=2 - вопрос №723975196615227661532 от Dashatatur1 31.05.2023 12:32

Question

Алгебра: Нужно доказать, log9 (6√6-15)^2+log27(6√6+15)^3=2

Dashatatur1 · Answer

log9 (6√6-15)^2 + log27(6√6+15)^3 =
= log3^2 (6√6-15)^2 + log3^3 (6√6+15)^3 =
= 1/2* log3 (6√6-15)^2 + 1/3* log3 (6√6+15)^3 =
= log3 ((6√6 - 15)^2)^1/2 + log3 ((6√6+15)^3)^1/3 =
= log3 | 6√6 - 15 |+ log3 (6√6 +15) = появление модуля (!)
= log3 (15 - 6√6) + log3 (15 + 6√6) =
= log3 ((15 - 6√6)* (15 + 6√6) ) =
= log3 (15^2 - (6√6)^2) =
= log3 (225 - 216) =
= log3 (9) =
= 2