Mister Exam
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How to use it?
- Inequation:
- (x^2+3^x-3)^5>(x^2+9^x-3^x)*5
- |4x-3|≥2x+3
-
cos(x)>=0,2
- 25*x<=6*5*x-5
-
Identical expressions
- log6(x^ two -5x)< two
- logarithm of 6(x squared minus 5x) less than 2
- logarithm of 6(x to the power of two minus 5x) less than two
- log6(x2-5x)<2
- log6x2-5x<2
- log6(x²-5x)<2
- log6(x to the power of 2-5x)<2
- log6x^2-5x<2
-
Similar expressions
- log6(x^2+5x)<2
log6(x^2-5x)<2 inequation
The solution
You have entered
[src]
/ 2 \
log\x - 5*x/
------------- < 2
log(6)
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} < 2$$
log(x^2 - 5*x)/log(6) < 2
Detail solution
Given the inequality:
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} < 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} = 2$$
Solve:
$$x_{1} = -4$$
$$x_{2} = 9$$
$$x_{1} = -4$$
$$x_{2} = 9$$
This roots
$$x_{1} = -4$$
$$x_{2} = 9$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$- \frac{41}{10}$$
substitute to the expression
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} < 2$$
$$\frac{\log{\left(\left(- \frac{41}{10}\right)^{2} - \frac{\left(-41\right) 5}{10} \right)}}{\log{\left(6 \right)}} < 2$$
but
Then
$$x < -4$$
no execute
one of the solutions of our inequality is:
$$x > -4 \wedge x < 9$$
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} < 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} = 2$$
Solve:
$$x_{1} = -4$$
$$x_{2} = 9$$
$$x_{1} = -4$$
$$x_{2} = 9$$
This roots
$$x_{1} = -4$$
$$x_{2} = 9$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$- \frac{41}{10}$$
substitute to the expression
$$\frac{\log{\left(x^{2} - 5 x \right)}}{\log{\left(6 \right)}} < 2$$
$$\frac{\log{\left(\left(- \frac{41}{10}\right)^{2} - \frac{\left(-41\right) 5}{10} \right)}}{\log{\left(6 \right)}} < 2$$
/3731\ log|----| \100 / < 2 --------- log(6)
but
/3731\ log|----| \100 / > 2 --------- log(6)
Then
$$x < -4$$
no execute
one of the solutions of our inequality is:
$$x > -4 \wedge x < 9$$
_____
/ \
-------ο-------ο-------
x1 x2
Rapid solution 2
[src]
(-4, 0) U (5, 9)
$$x\ in\ \left(-4, 0\right) \cup \left(5, 9\right)$$
x in Union(Interval.open(-4, 0), Interval.open(5, 9))
Rapid solution
[src]
Or(And(-4 < x, x < 0), And(5 < x, x < 9))
$$\left(-4 < x \wedge x < 0\right) \vee \left(5 < x \wedge x < 9\right)$$
((-4 < x)∧(x < 0))∨((5 < x)∧(x < 9))