Question

The value of $x$, if ${\log }_4(3x^2+11x)=1$

• A. $4$
• B. $\frac{1}{3}$
• C. $-4$
• D. $-\frac{1}{3}$

Answer 1

Answer: (B), (C)

The correct options are
B $\frac{1}{3}$
C $-4$

$3x^2+11x>0\Rightarrow x\in (-\infty ,-\frac{11}{3})\cup (0,\infty )$

${\log }_4(3x^2+11x)=1$
$\Rightarrow 3x^2+11x=4$
$\Rightarrow 3x^2+11x-4=0\Rightarrow (3x-1)(x+4)=0\Rightarrow x=-4,\frac{1}{3}$