Question

If ${\log }_{x}484-{\log }_{x}4+{\log }_{x}14641-{\log }_{x}1331=3$, then the value of $x$ is

• A. $1$
• B. $3$
• C. $11$
• D. None of these

Answer 1

The correct option is C $11$

As ${\log }_{x}484-{\log }_{x}4+{\log }_{x}14641-{\log }_{x}1331=3$

$\Rightarrow {\log }_x\left(\frac{484}{4}\right)+{\log }_{x}14641-{\log }_{x}1331=3$

$\Rightarrow {\log }_x{11}^2+{\log }_x{11}^4-{\log }_x{11}^3=3$

$\Rightarrow (2+4-3){\log }_{x}11=3\Rightarrow {\log }_{x}11=1$

$\Rightarrow 11$

Hence choice (c) is correct.