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  4. Let E= log 2( log 2 3)+ log 2( log 3 4)+ log 2( log 4 5)+ log 2( log 5 6)+ log 2( log 6 7)+ log 2( log 7 8), then 8E is equal to

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Q. Let $E=\log _2\left(\log _2 3\right)+\log _2\left(\log _3 4\right)+\log _2\left(\log _4 5\right)+\log _2\left(\log _5 6\right)+\log _2\left(\log _6 7\right)+\log _2\left(\log _7 8\right)$, then $8^E$ is equal to

Continuity and Differentiability

Solution:

$E =\log _2\left(\log _2 3\right)+ \log _2\left(\log _3 4\right)+\log _2\left(\log _4 5\right)+\log _2\left(\log _5 6\right) \text { [11th, 03-07-2011, J] }
+\log _2\left(\log _6 7\right)+\log _2\left(\log _7 8\right)=\log _2\left(\log _2 8\right)=\log _2 3 $
$\text { Hence, } 8^E=8^{\log _2 3}=2^{\log _2(3)^3}=(3)^3=27$