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.