The value of _ 2 _ 2 _ 4 256+2 _ 2 2 is: - Vidyadip

MCQ

The value of $\log _{2} \log _{2} \log _{4} 256+2 \log _{\sqrt{2}} 2$ is:

A
3
B
2
C
7
✓
5

✓

Answer

Correct option: D.

5

(d) 5
Explanation: Use the properties:
$\log _{a}(m)^{n}=n \log _{a} m$ and $\log _{a} a=1$
Consider, $\log _{2} \log _{2} \log _{4} 256+2 \log _{\sqrt{2}} 2$
$=\log _{2} \log _{2} \log _{4}(4)^{4}+2 \log _{\sqrt{2}}(\sqrt{2})^{2}$
$=\log _{2} \log _{2} 4+2(2)$
$=\log _{2} \log _{2}(2)^{2}+4$
$=\log _{2} 2+4$
$=1+4=5$

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