Mister Exam
log1/sqrt(5)(6^(x+1)-36^x)>=-2 inequation
The solution
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log(1) / x + 1 x\ ------*\6 - 36 / >= -2 ___ \/ 5
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{x} + 6^{x + 1}\right) \geq -2$$
(log(1)/sqrt(5))*(-36^x + 6^(x + 1)) >= -2
Detail solution
Given the inequality:
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{x} + 6^{x + 1}\right) \geq -2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{x} + 6^{x + 1}\right) = -2$$
Solve:
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
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{0} + 6^{1}\right) \geq -2$$
so the inequality is always executed
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{x} + 6^{x + 1}\right) \geq -2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{x} + 6^{x + 1}\right) = -2$$
Solve:
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
x0 = 0
$$\frac{\log{\left(1 \right)}}{\sqrt{5}} \left(- 36^{0} + 6^{1}\right) \geq -2$$
0 >= -2
so the inequality is always executed
Rapid solution
This inequality holds true always