Verify if the equation log2 (x)=-1 have solutions?

First, we'll take antilogarithm, to determine x. In this
case, this means to raise the given base of logarithm, namely 2, to the power
-1.

log2 (x) = -1 => x =
2^-1

We'll use the negative power
property:

2^-1 = 1/2

x =
1/2

Since x>0, then 1/2 represents the solution of
the equation.

Therefore, the given equation
has one solution x = 1/2.