2^(x^2)*13^(x-1)>=2 inequation

Given the inequality:
$$13^{x - 1} \cdot 2^{x^{2}} \geq 2$$
To solve this inequality, we must first solve the corresponding equation:
$$13^{x - 1} \cdot 2^{x^{2}} = 2$$
Solve:
$$x_{1} = 1$$
$$x_{2} = - \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - 1$$
$$x_{1} = 1$$
$$x_{2} = - \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - 1$$
This roots
$$x_{2} = - \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - 1$$
$$x_{1} = 1$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$\left(- \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - 1\right) + - \frac{1}{10}$$
=
$$- \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - \frac{11}{10}$$
substitute to the expression
$$13^{x - 1} \cdot 2^{x^{2}} \geq 2$$
$$13^{\left(- \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - \frac{11}{10}\right) - 1} \cdot 2^{\left(- \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - \frac{11}{10}\right)^{2}} \geq 2$$

 /                2\                      
 |/  11   log(13)\ |     21   log(13)     
 ||- -- - -------| |   - -- - ------- >= 2
 \\  10    log(2)/ /     10    log(2)     
2                   *13                   

one of the solutions of our inequality is:
$$x \leq - \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - 1$$

 _____           _____          
      \         /
-------•-------•-------
       x2      x1

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \leq - \frac{\log{\left(13 \right)}}{\log{\left(2 \right)}} - 1$$
$$x \geq 1$$