Question

The solution of the equation
${\log }_{101}{\log }_7(\sqrt{7+x}+\sqrt{x})=0$

• A. $3$
• B. $7$
• C. $9$
• D. $49$

Answer 1

Answer: (C)

$9$

${\log }_{101}{\log }_7(\sqrt{7+x}+\sqrt{x})=0$

$\Rightarrow {\log }_7(\sqrt{7+x}+\sqrt{x})={101}^0=1$

$\Rightarrow \sqrt{7+x}+\sqrt{x}=7^1=7$

$\Rightarrow \sqrt{7+x}=7-\sqrt{x}$

$\Rightarrow 7+x=49+x-14\sqrt{x}$ (Squaring both sides)

$\Rightarrow 42=14\sqrt{x}$

$\Rightarrow 3=\sqrt{x}$

$\Rightarrow 9=x$

Hence, C is the correct option.