What are the values of x in the following equation:

log(x)(6x+1)-log(x)=7

there should be 2 values.

OK.  Concentrating only on the first log, here's how it works out:

               log [  x · (6x + 1) ]  =  log (6x² + x) .

Now looking at the whole left side, it says

                          log (6x² + x)  - log (x)

which is            log [ (6x² + x) / x ]

                     =  log (6x + 1).

So now we have

                                            log (6x + 1)  =  7

Raise 10 to the
power of each side:            6x + 1  =  10⁷

                                              6x         =  9,999,999

                                                x         =  9,999,999 / 6

                                                           =  1,666,666.5       

This number works when you plug it into the original equation.

I'm sorry, but just now, I don't see where a second solution would come from.