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Solution of \log _{\left(\frac{1}{2}\right)}(x-4) \geqslant-2 \text { is }

Option: 1

\left ( -\infty ,8 \right )

 

 


Option: 2

\left ( 4 ,8 \right )


Option: 3

\left ( -\infty ,8 \right )


Option: 4

\left ( 4,8 \right ]


Answers (1)

best_answer

\quad \log _{\left(\frac{1}{2}\right)}(x-4) \geqslant-2

\Rightarrow(x-4) \leqslant\left(\frac{1}{2}\right)^{-2}                (As base < 1)

\begin{gathered} \Rightarrow x-4 \leqslant 4 \\ \Rightarrow x \leqslant 8 . \end{gathered}

Domain

x-4>0 \Rightarrow x>4

Intersection

 

\therefore x\epsilon \left ( 4,8 \right ]

Posted by

Gaurav

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