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.
