Question

If ${\log }_4\left(x\right)=12$, then ${\log }_2\left(\frac{x}{4}\right)$ is equal to

• A. $11$
• B. $48$
• C. $-12$
• D. $22$

Answer 1

The correct option is D $22$

If ${\log }_4\left(x\right)=12$ then,

$x=4^{12}$

$\frac{x}{4}=4^{11}$

Hence,

${\log }_2\left(\frac{x}{4}\right)={\log }_2\left(4^{11}\right)$

$={\log }_2\left({\left(2^2\right)}^{11}\right)$

$={\log }_2\left(2^{22}\right)$

$=22$

Hence option D is correct.