Question

5^х<=2 Решить неравенство

Answer 1

5^x ≤ 2 = x ≤ log5(2)

Answer 2

To solve the inequality $5^x \leq 2$, you need to find the range of values for $x$ that satisfy the inequality. Let's solve it step by step:

Step 1: Take the logarithm of both sides. Since the logarithm function is monotonically increasing, the inequality will remain unchanged.

$\log_5(5^x) \leq \log_5(2)$

Step 2: Simplify the left side using the property $\log_b(b^x) = x$.

$x \leq \log_5(2)$

Step 3: Calculate the value of $\log_5(2)$. You can use a calculator for this.

$\log_5(2) \approx 0.431$

Step 4: The solution to the inequality is $x \leq 0.431$. So any value of $x$ that is less than or equal to approximately 0.431 will satisfy the original inequality.

In interval notation, the solution is $x \in (-\infty, 0.431]$.