Mister Exam
log1/2*log5(x-2)>0 inequation
The solution
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[src]
log(1) log(x - 2) ------*---------- > 0 2 log(5)
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(x - 2 \right)}}{\log{\left(5 \right)}} > 0$$
(log(1)/2)*(log(x - 2)/log(5)) > 0
Detail solution
Given the inequality:
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(x - 2 \right)}}{\log{\left(5 \right)}} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(x - 2 \right)}}{\log{\left(5 \right)}} = 0$$
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
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(-2 \right)}}{\log{\left(5 \right)}} > 0$$
but
so the inequality has no solutions
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(x - 2 \right)}}{\log{\left(5 \right)}} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(x - 2 \right)}}{\log{\left(5 \right)}} = 0$$
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
$$\frac{\log{\left(1 \right)}}{2} \frac{\log{\left(-2 \right)}}{\log{\left(5 \right)}} > 0$$
0 > 0
but
0 = 0
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
This inequality has no solutions