Question

Log0,8(2x-4)<=log0,8(3x-5)

Answer 1

Решение задания приложено

Answer 2

To solve the inequality log₀.₈(2x-4) ≤ log₀.₈(3x-5), we need to be careful with logarithm properties.

The inequality log₀.₈(2x-4) ≤ log₀.₈(3x-5) can be rewritten using the logarithm property: logₐ(b) ≤ logₐ(c) if and only if b ≤ c.

So, applying this property to the given inequality:

2x - 4 ≤ 3x - 5

Now, let's isolate the x term:

2x - 3x ≤ -5 + 4

-x ≤ -1

To get rid of the negative coefficient in front of x, we multiply both sides by -1. But remember that when we multiply or divide an inequality by a negative number, the inequality sign flips:

x ≥ 1

Thus, the solution to the inequality is x ≥ 1.