The value of log220log280-log25log2320 is
5
6
7
8
10
Explanation for the correct answer:
Compute the required value:
Let S=log220log280-log25log2320
Write the numbers as the product of their prime factors
⇒ S=log222×5log224×5-log25log226×5
⇒ S=log222+log25log224+log25-log25log226+log25 ∵logab=loga+logb
⇒ S=2log22+log254log22+log25-log256log22+log25 ∵logam=mloga
⇒ S=8log222+6log22log25+log252-6log22log25-log252 ∵log22=1
⇒ S=812
⇒ S=8
Hence, the value of log220log280-log25log2320 is 8.
Hence, option D is the correct answer.