#### Answer

$x=1.5 $

#### Work Step by Step

Re-write the given equation as: $4=2^{2x-1}$
or, $2^{2} =2^{2x-1}$
Use the rule power rule: $a^p=a^q$ .
We can see that the base $a=2$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $ 2=2x-1 \\ 2x=3 \\ x=1.5 $