Equations And Inequalities Question 4
Solution set of the inequality $ {\log_3}((x+2)(x+4)) + \log_{1/3}(x+2) < \frac{1}{2}\log \sqrt{3}7,(1) $ is
Options:
A) $ (-2,-1) $
B) $ (-2,3) $
C) $ (-1,3) $
D) $ (3,\infty ) $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ (x+2)(x+4)>0,\ x+2>0\Rightarrow x>-2. $ Now (1) can be written as $ {\log_3}((x+2)(x+4)) - \log_3(x+2) < \frac{\frac{\log 7}{2}}{\frac{\log 3}{2}} $ $ \Rightarrow {\log_3}(x+4)<\log_3(7)\Rightarrow x+4<7\text{ or }x<-1. $
BETA
