Алгебра 10 класс. Логарифмы

5) 2
6) 0
7) какое неравенство?
8) 1
9) х = log(0.4)0.64, y = log(2.5)10
10) -1

5) y = log2 (3x - 5) -------> ОДЗ: (3x-5) >0 -----> x > 5\3
y = 0 -------> 2^0 = (3x - 5) ----> 3x = 6 ----> x = 2
6) log4 (3x^2-11) = log4 (3x-12) ---->
ОДЗ: (3x^2-11)>0 и (3x-12)>0 или -V(11\3)<x4
=> x > 4
(3x^2 - 11) = (3x - 12) -----> 3x^2 - 3x + 1 = 0 ---> D<0 --->
=> корней нет
7) log3 (2x+1) = log3 5 ----> ОДЗ: (2x+1)>0 ----> x > -1\2
(2x+1) = 5 -----> 2x = 4 ----> x = 2
8) log3 log4 [4^(1\3)] + 2 = log3 [1\3 * log4 4] + 2 =
= log3 (1\3 * 1) + 2 = log3 [3^(-1)] + 2 = (-1)*log3 3 + 2 = -1 + 2 = 1
9)
{ 5^x * 2^y = 80
{ log(V3) (x+y) = 2 ---> (x + y) = (V3)^2 ----> x + y = 3 ---> y = 3 - x
ОДЗ: (x + y) > 0
5^x * 2^(3-x) = 80 ----> 5^x * 2^3\2^x = 80 ----> (5\2)^x = 10
x = log(5\2) 10
y = 3 - log(5\2) 10 = log(5\2) [(5\2)^3] - log(5\2) 10 =
= log(5\2) [(125\8)\10] = log(5\2) (25\16)