Final answer:
To solve the equation log 2x + log (2x-1)=log3x for x, combine the logarithms on the left side of the equation, equate the expressions inside the logarithms, simplify the equation, and solve for x.
Step-by-step explanation:
To solve the equation log 2x + log(2x-1) = log 3x for x, we can use the property of logarithms that states: the logarithm of the product of two numbers is equal to the sum of their logarithms. Using this property, we can combine the logarithms on the left side of the equation:
log 2x(2x-1) = log 3x
Now, we can apply another property of logarithms that states: if the logarithms of two numbers are equal, then the numbers themselves are equal. Using this property, we can equate the expressions inside the logarithms:
2x(2x-1) = 3x
Simplifying the equation and solving for x, we get:
4x^2 - 2x = 3x
4x^2 - 5x = 0
x(4x - 5) = 0
Therefore, x = 0 or x = 5/4.