log[3](7x-3)>=log[3](5x)
and the question is?
log3 (7x-3)- log3 (5x)M=0
log3( (7x-3)/5x)>=0
then
(7x-3)/5x >=1 (Remember 30=1, so log3 1 =0)
7x-3>=5x
2x>=3
x>=3/2
To solve the inequality log[3](7x-3) >= log[3](5x), we can follow these steps:
Step 1: Use the property of logarithms that states log[a](b) >= log[a](c) if and only if b >= c, with the same base a.
Using this property, we can rewrite the inequality as (7x-3) >= 5x.
Step 2: Simplify the inequality by isolating the variable x on one side.
Start by subtracting 5x from both sides:
(7x-3) - 5x >= 0
Simplifying, we get:
2x - 3 >= 0
Step 3: Solve the inequality.
Add 3 to both sides:
2x >= 3
Finally, divide both sides by 2 to solve for x:
x >= 3/2
So, the solution to the inequality log[3](7x-3) >= log[3](5x) is x >= 3/2, or any value greater than or equal to 3/2.