Решите 1. (2/3)^x>1 1/2 2. 9^2x≤1/3 3. (1/7)^x^2-9≤1 4. 4^x+2^x+1-80<0 5. (1/3)^t<1/27

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(2/3)^x > 1 1/2
First convert 1 1/2 to an improper fraction: 3/2
So the inequality becomes:
(2/3)^x > 3/2
Now take the logarithm of both sides to solve for x:
x log(2/3) > log(3/2)
x > log(3/2) / log(2/3)
Now calculate the value of x using a calculator.

9^(2x) ≤ 1/3
Since 9 can be written as 3^2, the inequality becomes:
(3^2)^(2x) ≤ 1/3
3^(4x) ≤ 1/3
Now take the logarithm of both sides to solve for x:
4x log(3) ≤ log(1/3)
x ≤ log(1/3) / (4 log(3))
Now calculate the value of x using a calculator.

(1/7)^(x^2 - 9) ≤ 1
Take the logarithm of both sides:
(x^2 - 9) log(1/7) ≤ 0
(x^2 - 9)(log(1/7)) ≤ 0
Now solve for x.

4^x + 2^x + 1 - 80 < 0
Convert 80 to a power of 2: 2^6
So the inequality becomes:
4^x + 2^x + 1 - 2^6 < 0
Take the logarithm of both sides and solve for x.

(1/3)^t < 1/27
Convert 1/27 to a power of 3: 3^(-3)
So the inequality becomes:
(1/3)^t < 3^(-3)
Take the logarithm of both sides and solve for t.