Question

The set of possible values of $x$ is such that $5^x+{(2\sqrt{3})}^{2x}-169$is always positive is

• A. $[3,\infty )$
• B. $[2,\infty )$
• C. $(2,\infty )$
• D. None of these

Answer 1

The correct option is C

$(2,\infty )$

Explanation for the correct option.

Solve for the value of$x$ for which $5^x+{(2\sqrt{3})}^{2x}-169$is positive.

$\Rightarrow$$5^x+{(2\sqrt{3})}^{2x}>{13}^2$

$\Rightarrow$ $5^x+{12}^x>{13}^2$

Since $5^2+{12}^2={13}^2$

For $x>2,5^x+{12}^x>5^2+{12}^2={13}^2$

Hence, option C is the correct option.