Mister Exam
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How to use it?
- Inequation:
- log3^2x+2log3^2(5x-6)<=3log3(5x-6)*log3x
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sinx<=-(sqrt3/2)
- 9log7(x^2+x-2)<=10+log7((x-1)9/(x+2))
- log_(x-2)(24-6x)<log_(x-2)(2x-3)
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Identical expressions
- log3^ two x+2log3^2(5x- six)<=3log3(5x- six)*log3x
- logarithm of 3 squared x plus 2 logarithm of 3 squared (5x minus 6) less than or equal to 3 logarithm of 3(5x minus 6) multiply by logarithm of 3x
- logarithm of 3 to the power of two x plus 2 logarithm of 3 squared (5x minus six) less than or equal to 3 logarithm of 3(5x minus six) multiply by logarithm of 3x
- log32x+2log32(5x-6)<=3log3(5x-6)*log3x
- log32x+2log325x-6<=3log35x-6*log3x
- log3²x+2log3²(5x-6)<=3log3(5x-6)*log3x
- log3 to the power of 2x+2log3 to the power of 2(5x-6)<=3log3(5x-6)*log3x
- log3^2x+2log3^2(5x-6)<=3log3(5x-6)log3x
- log32x+2log32(5x-6)<=3log3(5x-6)log3x
- log32x+2log325x-6<=3log35x-6log3x
- log3^2x+2log3^25x-6<=3log35x-6log3x
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Similar expressions
- log3^2x-2log3^2(5x-6)<=3log3(5x-6)*log3x
- log3^2x+2log3^2(5x-6)<=3log3(5x+6)*log3x
- log3^2x+2log3^2(5x+6)<=3log3(5x-6)*log3x
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What you mean?
- x*log(3)^2 + 2*(5*x - 1*6)*log(3)^2 <= 3*log(3*x)*log(5*x - 1*6)/log(3)
- 2*(5*x - 1*6)*log(3)^2 + log(3)^(2*x) <= 3*log(3*x)*log(5*x - 1*6)/log(3)
- (5*x - 1*6)*log(3)^2*log(3)^(2*x + 2) <= 3*log(3*x)*log(5*x - 1*6)/log(3)
- (5*x - 1*6)*log(3)^2*log(3)^(2*x + 2) <= 3*log(3*x)*log(5*x - 1*6)/log(3)
log3^2x+2log3^2(5x-6)<=3log3(5x-6)*log3x inequation
The solution
You have entered
[src]
2 2 3*log(5*x - 6)*log(3*x)
log (3)*x + 2*log (3)*(5*x - 6) <= -----------------------
log(3)
$$x \log{\left(3 \right)}^{2} + 2 \cdot \left(5 x - 6\right) \log{\left(3 \right)}^{2} \leq \frac{3 \log{\left(3 x \right)} \log{\left(5 x - 6 \right)}}{\log{\left(3 \right)}}$$
x*log(3)^2 + 2*(5*x - 1*6)*log(3)^2 <= 3*log(3*x)*log(5*x - 1*6)/log(3)
Detail solution
Given the inequality:
$$x \log{\left(3 \right)}^{2} + 2 \cdot \left(5 x - 6\right) \log{\left(3 \right)}^{2} \leq \frac{3 \log{\left(3 x \right)} \log{\left(5 x - 6 \right)}}{\log{\left(3 \right)}}$$
To solve this inequality, we must first solve the corresponding equation:
$$x \log{\left(3 \right)}^{2} + 2 \cdot \left(5 x - 6\right) \log{\left(3 \right)}^{2} = \frac{3 \log{\left(3 x \right)} \log{\left(5 x - 6 \right)}}{\log{\left(3 \right)}}$$
Solve:
$$x_{1} = \mathtt{\text{(1.2341443119377384+0.5013184797315792j)}}$$
$$x_{2} = \mathtt{\text{(1.2341443119377384-0.5013184797315792j)}}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$x_0 = 0$$
$$2 \left(\left(-1\right) 6 + 5 \cdot 0\right) \log{\left(3 \right)}^{2} + \log{\left(3 \right)}^{2} \cdot 0 \leq \frac{3 \log{\left(3 \cdot 0 \right)} \log{\left(\left(-1\right) 6 + 5 \cdot 0 \right)}}{\log{\left(3 \right)}}$$
so the inequality is always executed
$$x \log{\left(3 \right)}^{2} + 2 \cdot \left(5 x - 6\right) \log{\left(3 \right)}^{2} \leq \frac{3 \log{\left(3 x \right)} \log{\left(5 x - 6 \right)}}{\log{\left(3 \right)}}$$
To solve this inequality, we must first solve the corresponding equation:
$$x \log{\left(3 \right)}^{2} + 2 \cdot \left(5 x - 6\right) \log{\left(3 \right)}^{2} = \frac{3 \log{\left(3 x \right)} \log{\left(5 x - 6 \right)}}{\log{\left(3 \right)}}$$
Solve:
$$x_{1} = \mathtt{\text{(1.2341443119377384+0.5013184797315792j)}}$$
$$x_{2} = \mathtt{\text{(1.2341443119377384-0.5013184797315792j)}}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$x_0 = 0$$
$$2 \left(\left(-1\right) 6 + 5 \cdot 0\right) \log{\left(3 \right)}^{2} + \log{\left(3 \right)}^{2} \cdot 0 \leq \frac{3 \log{\left(3 \cdot 0 \right)} \log{\left(\left(-1\right) 6 + 5 \cdot 0 \right)}}{\log{\left(3 \right)}}$$
2
-12*log (3) <= zoo
so the inequality is always executed