Question

Log5x (больше или равно <, =) -2

Answer 1

Ответ на фото ///////.

Answer 2

To solve the inequality log5(x) ≥ -2, we need to find the range of values for x that satisfy the inequality.

Recall that the logarithm function with base 5 takes positive values for positive inputs and is defined for all positive real numbers. The inequality states that the logarithm of x with base 5 is greater than or equal to -2.

To remove the logarithm, we can rewrite the inequality using its exponential form. The logarithm and exponential functions are inverse operations of each other, so:

log5(x) ≥ -2

is equivalent to:

5^(-2) ≤ x

Now, we can calculate 5^(-2):

5^(-2) = 1/5^2 = 1/25

So, the inequality becomes:

1/25 ≤ x

Therefore, the solution to the inequality is x greater than or equal to 1/25:

x ≥ 1/25

In interval notation, this can be expressed as [1/25, +∞), meaning all real numbers greater than or equal to 1/25 satisfy the original inequality.