Mister Exam
2log(5-x)>0 inequation
The solution
Detail solution
Given the inequality:
$$2 \log{\left(5 - x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$2 \log{\left(5 - x \right)} = 0$$
Solve:
Given the equation
$$2 \log{\left(5 - x \right)} = 0$$
$$2 \log{\left(5 - x \right)} = 0$$
Let's divide both parts of the equation by the multiplier of log =2
$$\log{\left(5 - x \right)} = 0$$
This equation is of the form:
By definition log
then
$$5 - x = e^{\frac{0}{2}}$$
simplify
$$5 - x = 1$$
$$- x = -4$$
$$x = 4$$
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$2 \log{\left(5 - x \right)} > 0$$
$$2 \log{\left(5 - \frac{39}{10} \right)} > 0$$
the solution of our inequality is:
$$x < 4$$
$$2 \log{\left(5 - x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$2 \log{\left(5 - x \right)} = 0$$
Solve:
Given the equation
$$2 \log{\left(5 - x \right)} = 0$$
$$2 \log{\left(5 - x \right)} = 0$$
Let's divide both parts of the equation by the multiplier of log =2
$$\log{\left(5 - x \right)} = 0$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$5 - x = e^{\frac{0}{2}}$$
simplify
$$5 - x = 1$$
$$- x = -4$$
$$x = 4$$
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$2 \log{\left(5 - x \right)} > 0$$
$$2 \log{\left(5 - \frac{39}{10} \right)} > 0$$
/11\
2*log|--| > 0
\10/ the solution of our inequality is:
$$x < 4$$
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