Mister Exam
|log3(x-4)|<1 inequation
The solution
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|log(x - 4)| |----------| < 1 | log(3) |
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
Abs(log(x - 4)/log(3)) < 1
Detail solution
Given the inequality:
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| = 1$$
Solve:
$$x_{1} = 7$$
$$x_{1} = 7$$
This roots
$$x_{1} = 7$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 7$$
=
$$6.9$$
substitute to the expression
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
$$\left|{\frac{\log{\left(-4 + 6.9 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
the solution of our inequality is:
$$x < 7$$
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| = 1$$
Solve:
$$x_{1} = 7$$
$$x_{1} = 7$$
This roots
$$x_{1} = 7$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 7$$
=
$$6.9$$
substitute to the expression
$$\left|{\frac{\log{\left(x - 4 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
$$\left|{\frac{\log{\left(-4 + 6.9 \right)}}{\log{\left(3 \right)}}}\right| < 1$$
1.06471073699243
---------------- < 1
log(3) the solution of our inequality is:
$$x < 7$$
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x1
Solving inequality on a graph
Rapid solution 2
[src]
(13/3, 7)
$$x\ in\ \left(\frac{13}{3}, 7\right)$$
x in Interval.open(13/3, 7)