Question

hello my question is prove that 4 log (16/5) +5l log (25/24)+3 log (81/80) = log 2

Answer 1

 7 log(16/15) +5 log( 25/24) +3log(81/80) 
=7{ log(16−log15} +5{ log 25−log24} +3{log81−log80} 
=7{ log2⁴−log(3×5)} +5{ log5²−log(8×3)} +3{log3⁴−log16×5)} 
=7{ 4log2−log3−log5} +5{ 2log5−log8−log3} +3{4log3−log16−log5} 
=28log2−7log3−7log5 +10log5−5log2³−5log3 +12log3−3log2⁴−3log5 
=28log2−7log3−7log5 +10log5−5×3log2−5log3 +12log3−3×4log2−3log5 
=28log2−7log3−7log5 +10log5−15log2−5log3 +12log3−12log2−3log5 
=28log2−15log2−12log2−7log3−5log3 +12log3−7log5 +10log5−3log5 
=(28log2−15log2−12log2)−(7log3+5log3 −12log3)−(7log5 −10log5+3log5) 
=log2 
=0.30103

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