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

If 2^y = 3, then:

(log to the base 2 of) 2^y = (log to the base 2 of) 3
                  or
                                      y = log to the base 2 of 3

Note that y turns out to be a constant here.
We need to identify the graph that depicts (log to the base 2) of x, and once we have that, draw a vertical line thru x = 3 to estimate y.

Only the 3rd graph qualifies here.  Note that all basic log graphs have an x-intercept of (1,0), as the 3rd graph does.

If we draw on the 3rd graph a vertical line thru x=3, we see that this vert. line intersects the curve at roughly y=1.5.