Question

The solution set of the inequality $5^{x+2}>{\left(\frac{1}{25}\right)}^{1/x}$ is

• A. (-2, 0)
• B. (-2, 2)
• C. (-5, 5)
• D. (0, $\infty$)

Answer 1

Answer: (D)

We have
$5^{x+2}>(\frac{1}{25}{)}^{1/x}\Rightarrow 5^{x+2}>5^{-\frac{2}{x}}\Rightarrow x+2>-\frac{2}{x}$
$[\because base5>1]$
$\Rightarrow x+2+\frac{2}{x}>0\Rightarrow \frac{x^2+2x+2}{x}>0\Rightarrow \frac{1}{x}>0$
$[\because x^2+2x+2>0\forall x\in R]$
$\Rightarrow x>0orx\in (0,\infty )$