????? log₆9, ???? ????????, ??? log₆2 = k.

___________________________________

?????, log₆9 = log₆3² = 2·log₆3 = 2·log₆⁶/₂ = 2(log₆6 - log₆2) = 2(1 - k).

?????: 2(1 - k).

?????? ????????? lg(x + 1.5) = -lgx.

______________________________

????? lg(x + 1.5) + lgx = 0. ???? ?? ??????? ??????? ? ????????? lgx(x + 1.5) = 0, ?? ???????? ??????? ??????????? ????????? ?????????. ?????? ????????? ??????? ??????????? ????????? ?????????:

?????? ? ???????? ?????: x = ½.

?????: x = ½.

?????? ????????? ^{log₂(9 - 2x)}/_{(3 - x)} = 1.
    __________________________________

????? ??????, ??? x ≠ 3 ? ????????? ????????? ???????????:

log₂(9 - 2^x) = 3 - x; ????? ?????????? ??????????? ?????????:

9 - 2^x = 2^{3 - x};

2^x + ⁸/_2^x - 9 = 0;

(2^x)² - 9·2^x + 8 = 0; ??????? ????? ??????????? ????????? ?????????:

2^x = 1 ??? 2^x = 8. ?.?. x = 0 ??? x = 3. ?? ??? ??? ??????? x = 3 ?? ???????? ? ??? ????????? ????????? (?? ???????? ??? ? ????? ??????), ?? ????? ????????????: x = 0.

?????: x = 0.

?????? ????????? log₅(x - 2) + log_√5(x³ - 2) + log_0.2(x - 2) = 4.

__________________________________________________

??????, ??? x > 2 (???). ?????, ?????? ??? ????????? ? ??????? ????????? 5:

log₅(x - 2) + 2·log₅(x³ - 2) - log₅(x - 2) = 4.

2·log₅(x³ - 2) = 4.

log₅(x³ - 2) = log₅25.

x³ - 2 = 25.

x³ = 27.

x = 3. ????? ???????? ??? ???.

?????: x = 3.