First, we'll use the properties of logarithms to simplify the equation.
log0.5(4x-1) - log0.5(7x-3) = 0
We can combine the two logarithms using the division property of logarithms:
log0.5[(4x-1) / (7x-3)] = 0
Now, we'll convert the logarithmic equation into an exponential equation:
0.5^0 = (4x-1) / (7x-3)
Since any number raised to the power of 0 is equal to 1, we have:
1 = (4x-1) / (7x-3)
Now, let's simplify the equation further by cross multiplying:
7x - 3 = 4x - 1
Subtracting 4x from both sides, we get:
3x - 3 = -1
Adding 3 to both sides, we get:
3x = 2
Dividing by 3, we find:
x = 2/3
Therefore, the solution to the equation log0.5(4x-1) - log0.5(7x-3) = 0 is x = 2/3.
First, we'll use the properties of logarithms to simplify the equation.
log0.5(4x-1) - log0.5(7x-3) = 0
We can combine the two logarithms using the division property of logarithms:
log0.5[(4x-1) / (7x-3)] = 0
Now, we'll convert the logarithmic equation into an exponential equation:
0.5^0 = (4x-1) / (7x-3)
Since any number raised to the power of 0 is equal to 1, we have:
1 = (4x-1) / (7x-3)
Now, let's simplify the equation further by cross multiplying:
7x - 3 = 4x - 1
Subtracting 4x from both sides, we get:
3x - 3 = -1
Adding 3 to both sides, we get:
3x = 2
Dividing by 3, we find:
x = 2/3
Therefore, the solution to the equation log0.5(4x-1) - log0.5(7x-3) = 0 is x = 2/3.