Prove that log 2+6 log 16/15 +12 log 25/24+7log 81/80=1
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log 2+ 6 log 16/15 + 12 log 25/24 + 7log 81/80=1
LHS=log 2+16 log 16/15 +12 log 25/24+7log 81/80
=log 2 +16 log 2^4 /(3*5) +12 log 5²/2³*3 + 7 log 3^4/2^4 * 5
=log 2 +16*(4log2-log3-log5)+ 12*(2 log 5-3log2-log 3)+7*( 4log3-4 log 2-log5)
=log 2+64log2-16log3-16log5 +24log 5-36log2-12log3+28log3-28 log2-7log5
= log2 +log 5
==log 2+log5)
=log { 2*5}
=log 10
=1=RHS
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