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

Question

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 (A) 4 (B) 8 (C) 27 (D) 36

Tardigrade Admin · Accepted Answer

E = log 2( log 2 3)+ log 2( log 3 4)+ log 2( log 4 5)+ log 2( log 5 6) text [11th, 03-07-2011, J] + log 2( log 6 7)+ log 2( log 7 8)= log 2( log 2 8)= log 2 3 text Hence, 8E=8 log 2 3=2 log 2(3)3=(3)3=27

Q. Let $E = lo g_{2} (lo g_{2} 3) + lo g_{2} (lo g_{3} 4) + lo g_{2} (lo g_{4} 5) + lo g_{2} (lo g_{5} 6) + lo g_{2} (lo g_{6} 7) + lo g_{2} (lo g_{7} 8)$ , then $8^{E}$ is equal to

4

8

27

36

$E = lo g_{2} (lo g_{2} 3) + lo g_{2} (lo g_{3} 4) + lo g_{2} (lo g_{4} 5) + lo g_{2} (lo g_{5} 6) [11th, 03-07-2011, J] < b r / > + lo g_{2} (lo g_{6} 7) + lo g_{2} (lo g_{7} 8) = lo g_{2} (lo g_{2} 8) = lo g_{2} 3$
$Hence, 8^{E} = 8^{l o g_{2} 3} = 2^{l o g_{2} (3)^{3}} = (3)^{3} = 27$

Q. Let E=log2​(log2​3)+log2​(log3​4)+log2​(log4​5)+log2​(log5​6)+log2​(log6​7)+log2​(log7​8), then 8E is equal to

4

8

27

36

E=log2​(log2​3)+log2​(log3​4)+log2​(log4​5)+log2​(log5​6) [11th, 03-07-2011, J] <br/>+log2​(log6​7)+log2​(log7​8)=log2​(log2​8)=log2​3 Hence, 8E=8log2​3=2log2​(3)3=(3)3=27

Q. Let $E = lo g_{2} (lo g_{2} 3) + lo g_{2} (lo g_{3} 4) + lo g_{2} (lo g_{4} 5) + lo g_{2} (lo g_{5} 6) + lo g_{2} (lo g_{6} 7) + lo g_{2} (lo g_{7} 8)$ , then $8^{E}$ is equal to

$E = lo g_{2} (lo g_{2} 3) + lo g_{2} (lo g_{3} 4) + lo g_{2} (lo g_{4} 5) + lo g_{2} (lo g_{5} 6) [11th, 03-07-2011, J] < b r / > + lo g_{2} (lo g_{6} 7) + lo g_{2} (lo g_{7} 8) = lo g_{2} (lo g_{2} 8) = lo g_{2} 3$
$Hence, 8^{E} = 8^{l o g_{2} 3} = 2^{l o g_{2} (3)^{3}} = (3)^{3} = 27$