Question

Log 1/3(5x-9)< или =log 1/3 4x

Answer 1

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Answer 2

ОДЗ 
5х   - 9 > 0 
4x > 0
x > 1,8
log₁/₃ (5x - 9)  ≤ log₁/₃ 4x 
 (5x - 9)  ≥  4x  
5х - 4х ≥ 9 
x ≥ 9 

Ответ: x ∈ [ 9;  +∞[

Answer 3

To solve the logarithmic inequality log base 1/3 of (5x - 9) ≤ log base 1/3 of 4x, we can apply the properties of logarithms.

Using the property that log base a of b is less than or equal to log base a of c if and only if b is less than or equal to c, we can write the inequality as:

5x - 9 ≤ 4x

Now, let's solve for x:

5x - 9 - 4x ≤ 0

x - 9 ≤ 0

x ≤ 9

Therefore, the solution to the logarithmic inequality log base 1/3 of (5x - 9) ≤ log base 1/3 of 4x is x ≤ 9.