Question

Решите неравенство (1/27)^x<9​

Answer 1

Ответ:

Пошаговое объяснение:

(1/27)^x<9​

(27)^(-x)<3²

(3)^(-3x)<3²

-3х < 2

x > - 2/3

Answer 2

To solve the inequality $(1/27)^x < 9$, we need to find the range of values for $x$ that satisfy the inequality.

Let's first simplify the inequality:

$(1/27)^x < 9$

To make the inequality easier to work with, we can rewrite 9 as $9/1$:

$(1/27)^x < (9/1)$

Now, let's simplify the left-hand side:

$(1/27)^x = 27^{-x}$

So, the inequality becomes:

$27^{-x} < 9$

Next, we can convert both sides of the inequality to have the same base. Since $27 = 3^3$, we can rewrite the inequality as follows:

$(3^3)^{-x} < 3^2$

Now, apply the power rule for exponents:

$3^{-3x} < 3^2$

Since the base is the same, we can compare the exponents:

$-3x < 2$

Now, divide both sides by -3, remembering to reverse the inequality since we're dividing by a negative number:

$x > \frac{-2}{3}$

So, the solution for the inequality is $x > \frac{-2}{3}$. This means any value of $x$ greater than $\frac{-2}{3}$ will satisfy the inequality.