Question

Solution set of the inequality:
$2{\left(25\right)}^x-5\left({10}^x\right)+2\left(4^x\right)\ge 0$ is

• A. $(-1,\infty )$
• B. $(0,\infty )$
• C. $(2,\infty )$
• D. none of these

Answer 1

The correct option is D none of these

$2{\left(25\right)}^x-5\left({10}^x\right)+2\left(4^x\right)\ge 0$
$\Rightarrow 2{\left(\frac{5}{2}\right)}^{2x}-5{\left(\frac{5}{2}\right)}^x+2\ge 0$
$\Rightarrow [{\left(\frac{5}{2}\right)}^x-2][2{\left(\frac{5}{2}\right)}^x-1]\ge 0$
$\Rightarrow {\left(\frac{5}{2}\right)}^x\ge 2$ or $0<{\left(\frac{5}{2}\right)}^x\le \frac{1}{2}$
Taking log on base 5/2
$\Rightarrow x\ge {\log }_{5/2}\left(2\right)$ or $x\le {\log }_{5/2}\left(0.5\right)$
Ans: D