1) 4^(2x -3) = 7^(2x -3)| :7^(2x -3)
(4/7)^(2x-3) = 1= (4/7)^0
2x -3 = 0
2x = 3
x = 1,5
2)5^x +125/5^x =750 | * 5^x
(5^x)² +125 -750*5^x = 0
5^x = y
y² -750 y +125 = 0
3) 2^(3-2x) -3*2^(1-x) ≥ -1
2^3*2^(-2x) -3*2^1*2^(-x) +1 ≥ 0
8*2^(-2x) -6*2^(-x) +1 ≥ 0
2^(-x) = y
8y² -6y +1 ≥ 0
корни: у1= 1/2 и у2 = 1/4
а) у≤ 1/4
2^-x ≤1/4
2^-x ≤ 2^-2
-x ≤ -2
x ≥ 2
б) y ≥ 1/2
2^-x ≥ 1/2
2^-x ≥ 2^-1
- x ≥ -1
x ≤ 1