Given the equation
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} = 2$$
transform
$$\frac{\log{\left(\frac{x \left(x + 3\right)}{4} \right)}}{\log{\left(2 \right)}} = 0$$
$$\frac{\log{\left(x^{2} + 3 x \right)}}{\log{\left(2 \right)}} - 2 = 0$$
Do replacement
$$w = \log{\left(x^{2} + 3 x \right)}$$
Expand brackets in the left part
-2 + w/log2 = 0
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{\log{\left(2 \right)}} = 2$$
Divide both parts of the equation by 1/log(2)
w = 2 / (1/log(2))
We get the answer: w = log(4)
do backward replacement
$$\log{\left(x^{2} + 3 x \right)} = w$$
substitute w: