Which logarithmic graph can be used to approximate the value of y in the equation 2y = 3?

2y = 3 does not involve either logs or exponential functions; are you sure you've copied it down correctly?  Perhaps you meant    2^y = 3.
                                                                                                                   log 3
If that's the case, take the log of both sides:  y log 2 = log 3, so that y =
                                                                                                                    log 2

If you were to graph y = log x, you could approx. the value of log 3 and that of log 2, divide log 3 by log 2, and then label your result with "y=".