Question

5001^(1-x) > 5000^(1-x) с решением

Answer 1

5001⁽¹⁻ˣ⁾>5000⁽¹⁻ˣ⁾

Так как 5001>5000 ⇒

Для соблюдения данного неравенства (1-x) должен быть >0 ⇒

1-x>0

x<1.

Ответ: х∈(-∞;1).

Answer 2

To solve the inequality $5001^{(1-x)} > 5000^{(1-x)}$, we need to find the range of values for $x$ that satisfy the inequality. Here's the step-by-step solution:

Step 1: Take the natural logarithm (ln) of both sides of the inequality. The inequality will remain unchanged since ln(x) is a monotonically increasing function:

$\ln(5001^{(1-x)}) > \ln(5000^{(1-x)})$

Step 2: Use the property of exponents that $\ln(a^b) = b \ln(a)$ to simplify the equation:

$(1-x) \ln(5001) > (1-x) \ln(5000)$

Step 3: Divide both sides of the inequality by $(1-x)$. We need to be cautious here because if $(1-x)$ is negative, we have to reverse the inequality sign:

$\ln(5001) > \ln(5000)$

Step 4: Evaluate the natural logarithms:

$x < \frac{\ln(5000)}{\ln(5001)}$

Now, calculating the right-hand side of the inequality:

$x < \frac{\ln(5000)}{\ln(5001)} \approx 0.21714$

Thus, the solution to the inequality is $x < 0.21714$.