The equation (2sinx+√3)log2(tgx)=0 can be written as a product of two expressions equal to zero:

1) 2sinx + √3 = 0
2) log2(tgx) = 0

Solving the first expression:
2sinx + √3 = 0
sinx = -√3/2

This means x is in either the second or third quadrant where sine is negative. Since sin(π/3) = √3/2, the solution for x is x = -π/3.

Solving the second expression:
log2(tgx) = 0
tgx = 2^0
tgx = 1

This implies x is in either the first or third quadrant where tan(x) = 1. The solution for x is x = π/4.

Therefore, the solution to the equation (2sinx+√3)log2(tgx) = 0 is x = -π/3, π/4.