Question

. Find the value of log 125+ log 216-3 log 30+log 100

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Answer 1

$log(125) + log(216) - 3 log(30) + log(100) \\ = log_{10}(125) + log_{10}(216) - 3 log_{10}(30) + log_{10}(100) \\ = log_{10}(125 \times 216) - 3 log_{10}(10 \times 3) + log_{10}( {10}^{2} ) \\ = log_{10}(27000) - 3( log_{10}(10) + log_{10}(3) ) + 2log_{10}(10) \\ = log_{10}( {30}^{3} ) - 3(1 + log_{10}(3) ) + 2 \\ = 3 log_{10}(30) - 3 - 3 log_{10}(3) + 2 \\ = 3 log_{10}(10 \times 3) - 3 log_{10}(3) - 1 \\ = 3( log_{10}(10) + log_{10}(3) ) - 3 log_{10}(3) - 1 \\ = 3 + 3 log_{10}(3) - 3 log_{10}(3) - 1 \\ = 3 - 1 \\ = 2$

Answer 2

Answer:

-2

Step-by-step explanation: