Question

If $A={\log }_2{\log }_2{\log }_{4}256+2{\log }_{\sqrt{2}}2$, then $A$ is equal to

• A. $2$
• B. $3$
• C. $5$
• D. $7$

Answer 1

Answer: (C)

$5$

Use the properties:

${\log }_a{\left(m\right)}^n=n{\log }_{a}m$ and ${\log }_{a}a=1$

Consider, ${\log }_2{\log }_2{\log }_{4}256+2{\log }_{\sqrt{2}}2$

$={\log }_2{\log }_2{\log }_4{\left(4\right)}^4+2{\log }_{\sqrt{2}}{\left(\sqrt{2}\right)}^2$

$={\log }_2{\log }_{2}4+2\left(2\right)$

$={\log }_2{\log }_2{\left(2\right)}^2+4$

$={\log }_{2}2+4$

$=1+4=5$.