Question

Log 1/3(4-x)<-2 решить неравенство

Answer 1

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Answer 2

To solve the inequality $\log_{\frac{1}{3}}(4-x) < -2$, we need to follow these steps:

Step 1: Rewrite the inequality using exponentials. Step 2: Solve the exponential inequality. Step 3: Check the solution.

Step 1: Rewrite the inequality using exponentials.

The logarithmic inequality $\log_{\frac{1}{3}}(4-x) < -2$ can be rewritten as:

$\frac{1}{3}^{-2} < 4 - x$.

Step 2: Solve the exponential inequality.

$\frac{1}{3}^{-2}$ is equal to $(\frac{1}{3})^{-2} = 3^2 = 9$.

So the inequality becomes:

$9 < 4 - x$.

Step 3: Solve for $x$.

Subtract 4 from both sides:

$9 - 4 < -x$.

$5 < -x$.

Now, to isolate $x$, we need to reverse the inequality. Remember that reversing an inequality means flipping the sign. When we multiply or divide both sides by a negative number, we flip the inequality sign.

Divide both sides by -1 (and don't forget to flip the sign):

$x < -5$.

So the solution to the inequality is $x < -5$.