Posted by **Sara** on Sunday, February 13, 2011 at 7:22pm.

Find the equation of a logarithmic function whose graph has x-intercept 8, a vertical asymptote at x=0, and which passes through the point (1/2,4)

- Math-Logarithmic function -
**Reiny**, Sunday, February 13, 2011 at 9:26pm
Since I see numbers 1/2 , 4, and 8 I will use

log_{2} as my logarithm

Since the y-axis 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

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