ln e^(x+2) = 5 + ln e^2

For the beginning, we'll use the power property of
logarithms:

ln e^(x+2) = (x+2)*lne, where ln e =
1

ln e^(x+2) = x+2

ln e^2 =
2*ln e = 2

Now, we'll rewrite the
equation:

x+2 = 5+2

We'll
eliminate like terms:

x =
5

Another manner of solving would be to
subtract ln e^(x+2) both sides:

0 = 5 + ln e^2 - ln
e^(x+2)

We'll subtract 5 both
sides:

ln e^2 - ln e^(x+2) =
-5

We'll use the quotient
property:

ln [e^2/e^(x+2)] =
-5

But e^2/e^(x+2) = e^(2-x-2) =
e^-x

ln e^-x = -5

-x*ln e =
-5

-x = -5

x =
5