Find all real solutions to the logarithmic equation ln (x) + ln (2) = 0?

First, we'll impose the constraint of existence of
ln(x):

x > 0

Since the
logarithms from the equation have matching bases, we'll apply the product property of
logarithms and we'll transform the sum of logarithms into a
product.

ln (x) + ln (2) = ln
(2x)

But ln (x) + ln (2) = 0 => ln (2x) =
0

We'll take antilogarithm and we'll
have:

2x = `e^0`

2x =
1

x =
`1/2`

Since the value of x is positive, then
we'll accept it as solution of the given equation: x = `1/2`
.