Mister Exam

lnx inequation

A inequation with variable

The solution

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log(x) > 0
$$\log{\left(x \right)} > 0$$
log(x) > 0
Detail solution
Given the inequality:
$$\log{\left(x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(x \right)} = 0$$
Solve:
Given the equation
$$\log{\left(x \right)} = 0$$
$$\log{\left(x \right)} = 0$$
This equation is of the form:
log(v)=p

By definition log
v=e^p

then
$$x = e^{\frac{0}{1}}$$
simplify
$$x = 1$$
$$x_{1} = 1$$
$$x_{1} = 1$$
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:
$$x_{0} < x_{1}$$
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
$$\log{\left(x \right)} > 0$$
$$\log{\left(\frac{9}{10} \right)} > 0$$
log(9/10) > 0

Then
$$x < 1$$
no execute
the solution of our inequality is:
$$x > 1$$
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Solving inequality on a graph
Rapid solution [src]
1 < x
$$1 < x$$
1 < x
Rapid solution 2 [src]
(1, oo)
$$x\ in\ \left(1, \infty\right)$$
x in Interval.open(1, oo)