math dilemma!is log<(x-6)*(x-6)>= 2log(x-6) ?what is the domain of this function?

Question

is log<(x-a)*(x-a)*...........n times>=nlog(x-a) always?

Answer 1

Let's consider log (x^2)

The domain of this function is all real numbers except for x=0

Now let's consider the domain of the function:

2*log(x)

The domain of this function is all x>0. (Notice that one cannot include x<0 because the log of a negative number is not defined.)

So, one would have to restrict the domain of the functions
log(x^2) and 2 log (x) to be all x>0 for the functions to be equal.

Answer 2

1) domain : x>6 since argument of log is only defined for >0
2) yes. log(x) + log (y) = log(x*y) for all x,y >0

Answer 3

Yes, log<(x-a)*(x-a)*...........n times>=nlog(x-a) always.