To solve the equation log 2x + log 3 = 2log (6/5), we can use logarithmic properties to simplify it. First, let's use the product rule of logarithms to combine the terms on the left side of the equation. The product rule states that log a + log b = log (a * b). Applying the product rule, we get: log (2x * 3) = 2log (6/5) Simplifying further, we have: log (6x) = log (6/5)^2 Now, we can equate the arguments of the logarithms since the bases are the same. This means: 6x = (6/5)^2 To simplify the right side, we square the fraction: 6x = 36/25 Next, we can solve for x by isolating it. Dividing both sides of the equation by 6 gives us: x = 36/25 * (1/6) Simplifying further, we get: x = 6/25 Therefore, the solution to the equation log 2x + log 3 = 2log (6/5) is x = 6/25.