MathLogarithmic function
posted by Sara on .
Find the equation of a logarithmic function whose graph has xintercept 8, a vertical asymptote at x=0, and which passes through the point (1/2,4)

Since I see numbers 1/2 , 4, and 8 I will use
log_{2} as my logarithm
Since the yaxis is an asymptote, there cannot be a horizontal shift of the standard log function, but there could be a vertical shift as well as a compression.
let the function by
y = alog_{2}x + k
point (8,0) is on it, so
0 = alog_{2}8 + k
0 = a(3) + k , (#1)
point (1/2,4 lies on it, so
4 = alog_{2}(1/2) + k
4 = a(1) + k , (#2)
subtract #1 from #2
4 = 4a
a = 1
then 0 = 3+k
k = 3
so one possible log function would be
y =  log_{2}x + 3