ln e^3 + ln 6x = 6

We'll use the product property of the
logarithms:

ln e^3 + ln 6x = ln
(6x*e^3)

We'll substitute the sum by the
product:

ln (6x*e^3) = 6

So,
we can write the expression above:

6x*e^3  =
e^6

We'll divide by e^3 both
sides:

6x = e^3

We'll divide
by 6 both sides:

x =
e^3/6

Since the result is positive, the equation has the
solution

x =
e^3/6