Question

How to graph y=log6(x-1)-5

Answer 1

The domain of the function is the set arguments (x in this case) for which the function is defined. The log function is only defined when its argument is greater than zero. So in other words the following condition must hold

x - 1 > 0

This can be rearranged to

x > 1

and that describes the domain of your function.

The range of log (any base) is +/- infinity. In your function the result of the log has five subtracted from it but that won't affect the range overall because, informally, "infinity - 5 = infinity" and "-infinity - 5 = -infinity." I put that stuff in quotation marks because it's technically abusive of the concept of infinity but it's a good intuition in this case.

P.S. If you want to calculate the log_6(x) you can use the following:

log_6(x) = y
x = 6^y
log(x) = y * log(6)
y = log(x)/log(6)

So your base 6 log can be computed by dividing the base 10 log with the log (base 10) of 6.