Question

If $13^{{\log }_{10}x}=338-x^{{\log }_{10}13}$, then the value of $(x+2)$ is equal to

• A. 13
• B. 15
• C. 17
• D. 102

Answer 1

Answer: (D)

$\text{ Given, }13^{{\log }_{10}x}=338-x^{{\log }_{10}13}\Rightarrow 13^{{\log }_{10}x}=169=13^2\left(14^{{\log }_{10}x}=x^{{\log }_{10}13}\right)$
$\therefore {\log }_{10}x=2$
$\therefore x=100\Rightarrow (x+2)=102$