Which logarithmic function is shown in the graph?

the answer is a = log2(x - 1) + 2

We use special traignels
we draw a line like the one with length 8
we get an equilateral triangle
now we draw a line perpendicular to the botttom side to get a right triangl (see attachment)

since equilateral triangles are 60 degrees, and 1/2 of 60 is 30
we have a 30,60, 90 triangle
if the hypotonuse is 2x then the longer leg is x√3 and the shorter leg is x
the longer leg is the apothem
so
hyptonuse=8=2x
4=x
4√3=apothem
so then we gots
height=4√3
base=4
area=1/2 times base times height=1/2 times 4 times 4√3=8√3
there rae 8 of those triangles so
8 times 8√3=64√3

the area is 64√3 square units