Question

give the equation of the vertical asymptote of g(x)=log(x-1)

Answer 1

To find your vetical asymptotes, use the following approach. Find the value that you are domain should not belong to. In your example. you have given a log function. A log function cannot take certain x values. Find them

Then the values which cannot be x are your asymptotes. For examples, refer here
http://www.purplemath.com/modules/asymtote.htm

Answer 2

*vertical

Answer 3

X=1 is the vertical asymptote
see the graph the equation log(x-1) approaches to -infinity as x approaches to 1
it will never touch the axis x=1 hence this is the vertical asymtote

i have assumed the base of log>1