Is -2ln e^2 + 1 = -3 ?

Let's verify the given
relation:

First, we'll use the power property of
logarithms:

-2ln e^2 = ln (e^2)^-2 = ln
1/e^4

We'll write 1 = ln
e

We'll re-write the
relation:

ln 1/e^4 + ln e =
-3

We'll use the product property of
logarithms:

ln (1/e^4)*e =
-3

ln e/e^4 = -3

ln 1/e^3 =
-3

ln e^-3 = -3

-3ln 3 =
-3

-3  = -3

So,
the given identity is true: -2ln e^2 + 1 = -3.