If A -log 2log 2log 4 256-2 log -2 2- then A is equal toA- 3B- 5C- 7D- 2

The correct option is B 5A=log_2 log_2 log_4 256 + 2 log_2_1/22 = log_2 log_2 log_4 4^4+2 ×1/ ( 1/2 )log_2 2 =log_2 log_2 4+4 = log_2 log_2 2^2 + 4 =log_2 2+4= ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Laws of Logarithms

If A =log 2lo...

Question

If $A = l o g_{2} l o g_{2} l o g_{4} 256 + 2 l o g_{\sqrt{2}} 2$ , then A is equal to

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Solution

The correct option is C 5
$A = l o g_{2} l o g_{2} l o g_{4} 256 + 2 l o g_{2_{\frac{1}{2}}} 2$
$= l o g_{2} l o g_{2} l o g_{4} 4^{4} + 2 \times \frac{1}{(\frac{1}{2})} l o g_{2} 2$
$= l o g_{2} l o g_{2} 4 + 4 = l o g_{2} l o g_{2} 2^{2} + 4$
$= l o g_{2} 2 + 4 = 1 + 4 = 5$

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If A=log2 log2 log4 256+2log√22, then A is equal to

The correct option is C 5A=log2 log2 log4 256+2log2122 =log2 log2 log4 44+2×1(12)log22 =log2 log24+4=log2 log2 22+4 =log22+4=1+4=5

If $A = l o g_{2} l o g_{2} l o g_{4} 256 + 2 l o g_{\sqrt{2}} 2$ , then A is equal to

The correct option is C 5
$A = l o g_{2} l o g_{2} l o g_{4} 256 + 2 l o g_{2_{\frac{1}{2}}} 2$
$= l o g_{2} l o g_{2} l o g_{4} 4^{4} + 2 \times \frac{1}{(\frac{1}{2})} l o g_{2} 2$
$= l o g_{2} l o g_{2} 4 + 4 = l o g_{2} l o g_{2} 2^{2} + 4$
$= l o g_{2} 2 + 4 = 1 + 4 = 5$