What transformation has changed the parent function f(x) = log2 x to its new appearance shown in the graph below? logarithmic graph passing through point negative 1, 3.

Assuming there are no vertical or horizontal stretches or any reflections (a picture would help)...

Understanding that log base 2 of 1 = 0, (that is 2 raised to the 0 power = 1) can help us figure out the transformation. So the coordinate is (1,0).

This has been shifted to the left 2 spots (to -1) and up 3 (to 3), therefore we can apply to get the new equation. 

log2(x+2) + 3.

So it would be a horizontal shift left 2 and a vertical shift up 3. (Again assuming no stretches/shrinks/reflections).