2 log 16 + 3 log 27 + 5 log 1/25

2 log 16 + 3 log 27 + 5 log 1/25

$2 log(16 ) + 3 log(27) + 5 log( frac{1}{25} ) \ \ = 2 log( {2}^{4} ) + 3 log( {3}^{3} ) + 5 log( {5}^{ - 2} ) \ = 4 times 2 log(2) + 3 times 3 log(3) + ( - 2) times 5 log(5) \ = 4 times 1 + 3 times 1 + ( - 2) times 1 \ = 4 + 3 + ( - 2) \ = 5$