Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 2\(cosx)>0
- ((x+6)/(x-6))*(((x-4)/(x+4))^2)+((x-6)/(x+6))*(((x+9)/(x-9))^2)>2*((x^2+36)/(x^2-36))
- -2x^3+3x-1>0
- 7^(-|x-3|)log(6x-x^2-7)^2>=1
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- log(one / two)*log(sqrt(five))*(x- four)>- one
- logarithm of (1 divide by 2) multiply by logarithm of ( square root of (5)) multiply by (x minus 4) greater than minus 1
- logarithm of (one divide by two) multiply by logarithm of ( square root of (five)) multiply by (x minus four) greater than minus one
- log(1/2)*log(√(5))*(x-4)>-1
- log(1/2)log(sqrt(5))(x-4)>-1
- log1/2logsqrt5x-4>-1
- log(1 divide by 2)*log(sqrt(5))*(x-4)>-1
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Similar expressions
- log1/2*logsqrt(5)*(x-4)>-1
- log(1/2)*log(sqrt(5))*(x+4)>-1
- log(1/2)*log(sqrt(5))*(x-4)>+1
- log(1/2)log(sqrt(5(x-4)))>-1
log(1/2)*log(sqrt(5))*(x-4)>-1 inequation
The solution
You have entered
[src]
/ ___\ log(1/2)*log\\/ 5 /*(x - 4) > -1
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) > -1$$
(log(1/2)*log(sqrt(5)))*(x - 4) > -1
Detail solution
Given the inequality:
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) > -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) = -1$$
Solve:
Given the equation:
Expand expressions:
Reducing, you get:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x \log{\left(2 \right)} \log{\left(5 \right)}}{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} = -1$$
Divide both parts of the equation by (2*log(2)*log(5) - x*log(2)*log(5)/2)/x
We get the answer: x = 4 + 2/(log(2)*log(5))
$$x_{1} = \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
$$x_{1} = \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
This roots
$$x_{1} = \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(\frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4\right)$$
=
$$\frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + \frac{39}{10}$$
substitute to the expression
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) > -1$$
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(-4 + \left(\frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + \frac{39}{10}\right)\right) > -1$$
the solution of our inequality is:
$$x < \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) > -1$$
To solve this inequality, we must first solve the corresponding equation:
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) = -1$$
Solve:
Given the equation:
log(1/2)*log(sqrt(5))*(x-4) = -1
Expand expressions:
2*log(2)*log(5) - x*log(2)*log(5)/2 = -1
Reducing, you get:
1 + 2*log(2)*log(5) - x*log(2)*log(5)/2 = 0
Expand brackets in the left part
1 + 2*log2log5 - x*log2log5/2 = 0
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x \log{\left(2 \right)} \log{\left(5 \right)}}{2} + 2 \log{\left(2 \right)} \log{\left(5 \right)} = -1$$
Divide both parts of the equation by (2*log(2)*log(5) - x*log(2)*log(5)/2)/x
x = -1 / ((2*log(2)*log(5) - x*log(2)*log(5)/2)/x)
We get the answer: x = 4 + 2/(log(2)*log(5))
$$x_{1} = \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
$$x_{1} = \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
This roots
$$x_{1} = \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(\frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4\right)$$
=
$$\frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + \frac{39}{10}$$
substitute to the expression
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(x - 4\right) > -1$$
$$\log{\left(\frac{1}{2} \right)} \log{\left(\sqrt{5} \right)} \left(-4 + \left(\frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + \frac{39}{10}\right)\right) > -1$$
/ 1 2 \ / ___\ -|- -- + -------------|*log(2)*log\\/ 5 / > -1 \ 10 log(2)*log(5)/
the solution of our inequality is:
$$x < \frac{2}{\log{\left(2 \right)} \log{\left(5 \right)}} + 4$$
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x1
Solving inequality on a graph
Rapid solution
[src]
/ 2*(1 + 2*log(2)*log(5))\ And|-oo < x, x < -----------------------| \ log(2)*log(5) /
$$-\infty < x \wedge x < \frac{2 \left(1 + 2 \log{\left(2 \right)} \log{\left(5 \right)}\right)}{\log{\left(2 \right)} \log{\left(5 \right)}}$$
(-oo < x)∧(x < 2*(1 + 2*log(2)*log(5))/(log(2)*log(5)))
Rapid solution 2
[src]
2*(1 + 2*log(2)*log(5))
(-oo, -----------------------)
log(2)*log(5)
$$x\ in\ \left(-\infty, \frac{2 \left(1 + 2 \log{\left(2 \right)} \log{\left(5 \right)}\right)}{\log{\left(2 \right)} \log{\left(5 \right)}}\right)$$
x in Interval.open(-oo, 2*(1 + 2*log(2)*log(5))/(log(2)*log(5)))