SOLUTION: Write the logarithmic function with x = 2 as its vertical asymptote and (3,0) as the x-intercept.

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Question 1159026: Write the logarithmic function with x = 2 as its vertical asymptote and (3,0) as the x-intercept.
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


For the logarithmic function y+=+a%2Alog%28%28x%29%29, the vertical asymptote is x=0. So a vertical asymptote at x=2 means the function is shifted 2 to the right.

So the function is y+=+a%2Alog%28%28x-2%29%29.

To find the constant multiplier a, substitute the coordinates of the x-intercept:

0+=+a%2Alog%28%283-2%29%29
0+=+a%2Alog%28%281%29%29
0+=+a%2A0

That says a can be any constant.

Here is a graph of a*log(x-2) with 3 values of a -- 1 (red), 3 (green), and -2(blue).

graph%28400%2C400%2C-2%2C10%2C-10%2C10%2Cln%28x-2%29%2C3%2Aln%28x-2%29%2C-2%2Aln%28x-2%29%29