Question

The range of $x$ satisfying $3^x+2^{2x}\ge 5^x$ is

• A. $(-\infty ,2]$
• B. $[2,\infty )$
• C. $[0,2]$
• D. $\left\{2\right\}$

Answer 1

The correct option is A $(-\infty ,2]$

Given : $3^x+2^{2x}\ge 5^x$
$\Rightarrow 3^x+4^x\ge 5^x\Rightarrow {\left(\frac{3}{5}\right)}^x+{\left(\frac{4}{5}\right)}^x\ge 1\Rightarrow {\left(\frac{3}{5}\right)}^x+{\left(\frac{4}{5}\right)}^x\ge {\left(\frac{3}{5}\right)}^2+{\left(\frac{4}{5}\right)}^2\Rightarrow x\le 2$