3log2(x)>3 inequation

Given the inequality:
$$3 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}} > 3$$
To solve this inequality, we must first solve the corresponding equation:
$$3 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}} = 3$$
Solve:
Given the equation
$$3 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}} = 3$$
$$\frac{3 \log{\left(x \right)}}{\log{\left(2 \right)}} = 3$$
Let's divide both parts of the equation by the multiplier of log =3/log(2)
$$\log{\left(x \right)} = \log{\left(2 \right)}$$
This equation is of the form:

log(v)=p

By definition log

v=e^p

then
$$x = e^{\frac{3}{3 \frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$x = 2$$
$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$3 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}} > 3$$
$$3 \frac{\log{\left(\frac{19}{10} \right)}}{\log{\left(2 \right)}} > 3$$

     /19\    
3*log|--|    
     \10/ > 3
---------    
  log(2)     

Then
$$x < 2$$
no execute
the solution of our inequality is:
$$x > 2$$

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       x1