(1/3)^x<1/sqrt(3) inequation

Given the inequality:
$$\left(\frac{1}{3}\right)^{x} < \frac{1}{\sqrt{3}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{1}{3}\right)^{x} = \frac{1}{\sqrt{3}}$$
Solve:
Given the equation:
$$\left(\frac{1}{3}\right)^{x} = \frac{1}{\sqrt{3}}$$
or
$$- \frac{1}{\sqrt{3}} + \left(\frac{1}{3}\right)^{x} = 0$$
or
$$\left(\frac{1}{3}\right)^{x} = \frac{\sqrt{3}}{3}$$
or
$$\left(\frac{1}{3}\right)^{x} = \frac{\sqrt{3}}{3}$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{1}{3}\right)^{x}$$
we get
$$v - \frac{\sqrt{3}}{3} = 0$$
or
$$v - \frac{\sqrt{3}}{3} = 0$$
Expand brackets in the left part

v - sqrt3/3 = 0

Divide both parts of the equation by (v - sqrt(3)/3)/v

v = 0 / ((v - sqrt(3)/3)/v)

do backward replacement
$$\left(\frac{1}{3}\right)^{x} = v$$
or
$$x = - \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
$$x_{1} = \frac{\sqrt{3}}{3}$$
$$x_{1} = \frac{\sqrt{3}}{3}$$
This roots
$$x_{1} = \frac{\sqrt{3}}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\sqrt{3}}{3}$$
=
$$- \frac{1}{10} + \frac{\sqrt{3}}{3}$$
substitute to the expression
$$\left(\frac{1}{3}\right)^{x} < \frac{1}{\sqrt{3}}$$
$$\left(\frac{1}{3}\right)^{- \frac{1}{10} + \frac{\sqrt{3}}{3}} < \frac{1}{\sqrt{3}}$$

        ___     ___
 1    \/ 3    \/ 3 
 -- - ----- < -----
 10     3       3  
3             

but

        ___     ___
 1    \/ 3    \/ 3 
 -- - ----- > -----
 10     3       3  
3             

Then
$$x < \frac{\sqrt{3}}{3}$$
no execute
the solution of our inequality is:
$$x > \frac{\sqrt{3}}{3}$$

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        /
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       x1