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11 * 4^(log2 9) =
= 11 * (2^2)^(log2 9) =
= 11 * 2^(2 * log2 9) =
= 11 * 2^(log2 (9^2)) =
= 11 * 9^2 = 891

log6 5 * log25 216 =
= log6 5 * log(5^2) (6^3) =
= log6 5 * (1/2) * 3 * log5 6 =
= 3/2 * log6 5 * 1/log6 5 = 3/2

5 * log9 (9^(1/3)) - log(7^3) 49 =
= 5 * (1/3) * log9 9 - (1/3) * 2 * log7 7 =
= 5/3 - 2/3 = 3/3 = 1

log2 (12 - 4x) = 5 ---> ОДЗ: (12 - 4x)>0 ---> x < 3
(12 - 4x) = 2^5
4x = 12 - 2^5 = 12 - 25 = - 13
x = - 13/4

log8 (4x + 7) = log8 3 ---> ОДЗ: (4x + 7)>0 ---> x > - 7/4
(4x + 7) = 3
4x = - 4
x = - 1

8^(log8 (x + 26)) = 3 ---> ОДЗ: (x + 26)>0 ---> x > - 26
(x + 26) = 3
x = - 23

8^(log2 (x + 26)) = 3 ---> ОДЗ: (x + 26)>0 ---> x > - 26
(2^3)^(log2 (x + 26)) = 3
2^(3 * log2 (x + 26)) = 3
2^(log2 ((x + 26)^3)) = 3
(x + 26)^3 = 3
x + 26 = 3^(1/3)
x = 3^(1/3) - 26

log8 (2^(8x - 4)) = 4
2^(8x - 4) = 8^4
2^(8x - 4) = (2^3)^4 = 2^12
(8x - 4) = 12
8x = 16
x = 2

log7 (11x + 5) - log7 2 = log7 19 ---> ОДЗ: (11x-5)>0 ---> x > 5/11
log7 [(11x + 5) / 2] = log7 19
(11x + 5)/2 = 19
11x = 19*2 - 5 = 33
x = 3

log2 (x + 5) + log2 23 >= log2 69 ---> ОДЗ: x > - 5
log2 [(x + 5) * 23] >= 69
(x + 5) * 23 >= 69
(x + 5) >= 3
x >= - 2

log(1/7) (9 - x) + log(1/7) 1/x =< log(1/7) (1/x - x + 8)
ОДЗ: (9-x)> 0 ---> x < 9
1/x > 0 ---> x > 0
1/x - x + 8 > 0 ---> (1 - x^2 + 8x)/x > 0 ---> x ...
log(1/7) [(9 - x) * 1/x] =< log(1/7) (1/x - x + 8)
[(9 - x) * 1/x] >= (1/x - x + 8)
(9 - x)/x >= (1 - x^2 + 8x)/x
(9 - x - 1 + x^2 - 8x)/ x >= 0
(x^2 - 9x + 8) / x >= 0
(x - 1)(x - 8) / x >= 0
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