Question

Решите неравенство: log0,1х ≤- 1/2

Answer 1

Решение неравенства на фото

Answer 2

To solve the inequality: log₀.₁x ≤ -½, we need to rewrite it in exponential form, as logarithms and exponents are inverse operations. The base of the logarithm is 0.1, so we have:

log₀.₁x ≤ -½

Now, we can express the inequality in exponential form:

0.1^(-½) ≤ x

Next, evaluate 0.1^(-½):

0.1^(-½) = 1 / √0.1 = 1 / 0.31622776601683794 ≈ 3.1622776601683795

So the inequality becomes:

3.1622776601683795 ≤ x

Therefore, the solution for the inequality is x ≥ 3.1622776601683795.