To solve the equation log3(sin(2x)) = log3(cos(x)), we can use the fact that if two logs with the same base are set equal to each other, then the arguments must be equal as well.

Therefore, we have:

sin(2x) = cos(x)

Using the trigonometric identity sin(2x) = 2sin(x)cos(x), we can rewrite the equation as:

2sin(x)cos(x) = cos(x)

Now we have:

2sin(x) = 1

sin(x) = 1/2

This means that x could equal π/6, or 30 degrees, or any other angle that gives sin(x) = 1/2.

Therefore, the solution to the equation log3(sin(2x)) = log3(cos(x)) is x = π/6 + 2nπ, where n is an integer.