Given the inequality:
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(\frac{1}{3} \right)} = \log{\left(\frac{1}{3} \right)}$$
Solve:
$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
$$\log{\left(\frac{1}{3} \right)} \leq \log{\left(\frac{1}{3} \right)}$$
-log(3) -log(3)
---------- ----------
/92411\ <= /96441\
log|-----| log|-----|
\ 1000/ \ 1000/
the solution of our inequality is:
$$x \leq 1$$
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x_1