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  4. The absolute value of sum of real solutions of log 2|x2+5 x+4|= log 2 3+ log 2|x+1| is

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Q. The absolute value of sum of real solutions of $\log _2\left|x^2+5 x+4\right|=\log _2 3+\log _2|x+1|$ is

Continuity and Differentiability

Solution:

$\log _2 \frac{|( x +1)( x +4)|}{| x +1|}=\log _2 3$
$|x+4|=3 $
$x+4=-3,+3 $
$x=-7,-1 \text { (rejected) }$
$\Rightarrow x=-7 $