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  4. Solution set of the inequality log 3(x+2)(x+4)+ log 1 / 3(x+2) < (1/2) log √3 7(1) is

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Q. 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

Linear Inequalities

Solution:

$(x+2)(x+4) > 0 . x+2 > 0$
$ \Rightarrow x > -2$
Now (1) can be written as
$\log _{3}(x+2)(x+4)-\log _{3}(x+2) < \frac{(\log 7) / 2}{(\log 3) / 2}$
$\Rightarrow \log _{3}(x+4) < \log _{3} 7 $
$\Rightarrow x+4 < 7$ or $x < 3$