ln e^3 + ln e^3x = 6

Let's try the following method. We'll subtract ln e^3 both
sides:

ln e^3x = 6 - ln
e^3

We'll re-write 6 as:

6 =
6*1

We'll substitute the value 1 by ln
e.

6 = 6*ln e

We'll use the
power property of the logarithms:

6 = ln
e^6

We'll re-write the
equation:

ln e^3x = ln e^6 - ln
e^3

Because the bases are matching, we'll transform the
difference of logarithms from the right side, into a
quotient:

ln e^3x = ln
(e^6/e^3)

Because the bases are matching, we'll apply the
one to one property:

e^3x =
e^(6-3)

e^3x = e^3

Because the
bases are matching, we'll apply the one to one property:

3x
= 3

We'll divide by 3 both
sides:

x =
1