Question

If $x$ satisfies ${\log }_3(2x+1)<{\log }_{3}5$, then $x$ contains the interval(s)

• A. $(-\frac{1}{2},0)$
• B. $(0,2)$
• C. $[1,2)$
• D. $(2,3)$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $(-\frac{1}{2},0)$
B $(0,2)$
C $[1,2)$

${\log }_3(2x+1)<{\log }_{3}5$, where, $2x+1>0\Rightarrow x>-\frac{1}{2}$
$\Rightarrow 2x+1<5$
$\Rightarrow x<2$
$\therefore x\in (-\frac{1}{2},2)$
Ans: A,B,C