Question

Log7(5x-9)>=log7 4x​

Answer 1

$log_{7} (5x-9)\geq log_{7} (4x)$

ОДЗ:

$\left \{ {{5x-9\geq 0} \atop {4x\geq 0}} \right.$     $\left \{ {{x\geq 1.8} \atop {x\geq 0}} \right.$     x ∈ [1.8;  +oo).

$5x-9 \geq 4x\\5x-4x \geq 9\\1x \geq 9 = > Otvet: [9;+oo).$

Answer 2

To solve the inequality log₇(5x - 9) ≥ log₇(4x), we can start by using the properties of logarithms to simplify the expression. Here's the step-by-step solution:

1. Start with the given inequality: log₇(5x - 9) ≥ log₇(4x).

2. Apply the property of logarithms that states logₐ(b) ≥ logₐ(c) if and only if b ≥ c, where a > 0, a ≠ 1, b > 0, and c > 0. Using this property, we can drop the logarithm notation and rewrite the inequality as follows: 5x - 9 ≥ 4x.

3. Now, we can solve the inequality for x. Subtract 4x from both sides of the inequality: 5x - 4x - 9 ≥ 0.

4. Simplify the expression: x - 9 ≥ 0.

5. Add 9 to both sides of the inequality: x ≥ 9.

Therefore, the solution to the inequality log₇(5x - 9) ≥ log₇(4x) is x ≥ 9.