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Question

Let n be an integer greater than 1 and let an=1logn1001 if b=a3+a4+a5+a6 and c=a11+a12+a13+a14+a15. Then value of (bc) is equal to

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Solution

an=1logn1001
logxP=logyPlogyx
b=a3+a4+a5+a6
=1log31001+1log41001+1log51001+1log61001
=log23log21001+log24log21001+log25log21001+log26log21001
=log2(3×4×5×6)log21001 ( logm+logn=logmn)
=log2(360)log21001
Similarly c=a11+a12+a13+a14+a15
=log2(11×12×13×14×15)log2(1001)
=log2(336336)log2(1001)
bc=log2360log21001log2(336336)log2(1001)
log2(360×336336)/log21001 ( logn1 n=logm/n)
=log2(360336336)log2(1001)

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