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  • Which values of x satisfy the inequality <img alt="\mathrm{3^{x+2}>\left ( \frac{1}{9} \right )^{\frac{1}{x}}}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%5

Which values of x satisfy the inequality \mathrm{3^{x+2}>\left ( \frac{1}{9} \right )^{\frac{1}{x}}}?

Option: 1

(0,1)


Option: 2

(-1,0)


Option: 3

(-∞,0)


Option: 4

R


Answers (1)

best_answer

\\3^{x+2}>\left ( \frac{1}{9} \right )^{\frac{1}{x}} \\ \\3^{x+2}>(3^{-2})^{\frac{1}{x}} \\ \text{Now as the base is 3, which is greater than 1, so we can remove the base directly}\\ \Rightarrow x+2 > \frac{-2}{x} \\\mathrm{=x^2+2x+2 >0}\\ As\,\,D<0, \text{so it is always positive}\\ x \in R

 

Note: If base < 1, we can remove the base from both sides, but the direction of inequality changes in such a case

Posted by

Ritika Jonwal

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