Question

9^х -10* 3^х+1 +81 >=  0

Answer 1

Решение смотри на фото

Answer 2

To solve the inequality 9^x - 10 * 3^(x+1) + 81 >= 0, you can start by simplifying it.

First, notice that 81 can be expressed as 9^2, so the inequality becomes:

9^x - 10 * 3^(x+1) + 9^2 >= 0

Now, you can use a substitution to simplify the inequality. Let's set y = 3^x:

y = 3^x

Now, the inequality becomes:

y^2 - 10 * 3 * y + 9^2 >= 0

This is a quadratic inequality in terms of y. You can solve it by factoring or by using the quadratic formula. Factoring is the easiest way in this case:

(y - 9)(y - 9) >= 0

Now, you have a quadratic expression factored. The solution to this inequality is all the values of y that make it greater than or equal to zero.

The only real solution to this inequality is y = 9, as this makes both factors non-negative.

Now, remember that y = 3^x, so:

3^x = 9

To solve for x, take the logarithm of both sides:

x * log(3) = log(9)

x = log(9) / log(3)

Using common logarithms (base 10):

x ≈ 2

So, the solution to the inequality is x ≈ 2.