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Solution of   \log _{5}(x-2) \geqslant \log _{5}(2 x)

 

Option: 1

\left ( -\infty ,-2 \right )

 

 

 


Option: 2

\left ( 3, \infty \right )


Option: 3

\left ( 0, \infty \right )


Option: 4

\phi


Answers (1)

best_answer

\log _{5}(x-2) \geqslant \log _{5}(2 x)

As base > 1

\begin{aligned} &\Rightarrow(x-2) \geqslant 2 x \\ &\Rightarrow-2 \geqslant x \\ &\Rightarrow \quad x \leqslant-2 \end{aligned}__________(i)

Domains:

\log _{5}(x-2) \Rightarrow x-2>0 \Rightarrow x>2

And

\log _{5}(2 x) \Rightarrow 2 x>0 \Rightarrow x>0

Answer is intersection of (i) with domains

 

So Answer =\phi

Posted by

Ritika Kankaria

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