Question

2 - 3^(-x) >0 решить неравенство

Answer 1

Ответ:

Объяснение:

$2-3^{-x}>03^{-x}-log_3(2)$

Answer 2

To solve the inequality 2 - 3^(-x) > 0, we can begin by isolating the exponential term on one side of the inequality:

2 - 3^(-x) > 0

2 > 3^(-x)

Next, we can take the logarithm of both sides of the inequality to isolate x:

ln(2) > ln(3^(-x))

ln(2) > -x * ln(3)

x * ln(3) > -ln(2)

x > -ln(2)/ln(3)

Therefore, the solution to the inequality 2 - 3^(-x) > 0 is:

x > -ln(2)/ln(3)

We can verify this solution by plugging in a few values for x. For example, if we choose x = 0, we get:

2 - 3^(-0) = 2 - 1 = 1 > 0

This shows that x = 0 is not a solution to the inequality. If we choose x = 1, we get:

2 - 3^(-1) = 2 - 1/3 = 5/3 > 0

This shows that x = 1 is a solution to the inequality. Finally, if we choose x = -1, we get:

2 - 3^1 = 2 - 3 = -1 < 0

This shows that x = -1 is not a solution to the inequality. Therefore, the solution set for the inequality is:

x > -ln(2)/ln(3)