Question

For logarithm ${\log }_{0.2}$ $\frac{x+2}{x}$ to be defined. Which of the following is/are true?

• A. x ∈ (-∞, -2)
• B. x ∈ (0, ∞)
• C. x ∈ (-2, 0)
• D. x ∈ R

Answer 1

Answer: (A), (B)

The correct options are
A

x ∈ (-∞, -2)

B

x ∈ (0, ∞)

${\log }_{0.2}$ $\frac{x+2}{x}$ $\le$ 1

For log to be defined

$\frac{x+2}{x}$ > 0

x > 0 and x < -2

x ∈ $(-\infty ,-2)$ U (0,$\infty$)