(11*(3^(x-1))-31)/(4*(9^x)-11*(3^(x-1))-5)≥5

Предыдущий
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вопрос

To solve this inequality, we can first simplify the expression:

Given: (11(3^(x-1))-31)/(4(9^x)-11*(3^(x-1))-5) ≥ 5

Let's substitute:
Let y = 3^(x-1)

(11y - 31)/(4(9y) - 11y - 5) ≥ 5
(11y - 31)/(36y - 11y - 5) ≥ 5
(11y - 31)/(25y - 5) ≥ 5

Now, we will multiply both sides by (25y-5) to simplify the expression:

(11y - 31) ≥ 5(25y - 5)
11y - 31 ≥ 125y - 25
-114*y ≥ 6
y ≤ -1/19

Now, we substitute back y = 3^(x-1):

3^(x-1) ≤ -1/19
x-1 ≤ log3(-1/19)
x ≤ log3(-1/19) + 1

Therefore, the solution to the inequality is x ≤ log3(-1/19) + 1. Since the logarithm of a negative number is undefined, there is no real solution to this inequality.