Which set?

Algebra Level 3

The set of values of x satisfying simultaneously the inequalities $\dfrac { \sqrt { (x-8)(x-2) } }{ \log _{ .3 }{ (\frac { 10 }{ 7 } } (\log _{ 2 }{ 5 } -1)) } \ge 0$ and $2^{x-3} - 3!>0$ is :

an empty set a unit set a set consisting of exactly 2 elements an infinite set

1 solution

Yashas Ravi
Jun 2, 2020

The denominator is less than $0$ , so the numerator of the inequality with the logarithm has to be less than or equal to $0$ . The only values that satisfy this is $x = 8$ and $x=2$ , but $x=2$ does not satisfy the inequality with the exponent so $x=8$ is the only set so the set of values for $x$ is a unit set since there is only one solution, $x=8$ , satisfying both inequalities.

Which set?

1 solution

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