Question

The set of real values x satisfying ${\log }_{0.3}$ (x-3)>3.

• A. x>3
• B. x>3.027
• C. x > 0.027
• D. x ∈ (3, 3.027)

Answer 1

The correct option is D

x ∈ (3, 3.027)

${\log }_{0.3}$ (x - 3) > 3 ---------------(1)

For log to be defined x - 3 > 0

x > 3 ----------------(2)

Base of the log lies between 0 to 1, from the given logarithm inequality we get,

(x - 3) < $(0.3{)}^3$

x < 3 + 0.027

x < 3.027 -----------------(3)

From equation 2 and equation 3, we see that x ∈ (3,3.027)

So, set of red values x satisfying the ${\log }_{0.3}$ (x - 3) > 3 is x ∈ (3,3.027)