Question

Find the set of values of x for which logarithm expression ${\log }_2$ ($x^2$ - x - 6) + ${\log }_{0.5}$ (x - 3) is defined.

• A. x ∈ (-∞, -2)
• B. x ∈ (3, ∞)
• C. x ∈ (-∞, -2) ∪ (3, ∞)
• D. None of these

Answer 1

The correct option is B

x ∈ (3, ∞)

Expression ${\log }_2$ ($x^2$ - x - 6) + ${\log }_{0.5}$ (x - 3) to be defined

$x^2$ - x - 6 > 0 and x - 3 > 0

Common port between these two conditions x ∈ (3,$\infty$)

So, above given logarithmic expression is defined only in the interval of x ∈ (3,$\infty$)