Question

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

Answer 1

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$\: \: \: \: \: \: \bold{ log \: 125 + log \: 216 - 3 \: log \: 30 \: + log \: 100} \\ \\ \bold{= log \: (5) {}^{3} + log \: (6) {}^{3} - 3 \: log \: (5 \times 6) + log \: (10) {}^{2} }\\ \\ \bold{= 3 \: log \: 5 + 3 \: log \: 6 \: - 3 \: log \: 5 - 3 \: log \: 6 + 2 \: log \: 10 }\\ \\ \bold{= 3 \: log \: 5 - 3 \: log \: 5 + 3 \: log \: 6 - 3 \: log \: 6 + 2 \: log \: 10} \\ \\ \bold{ = 2 \: log \: 10 }\\ \\ \bold{ = 2 \times 1 \: \: \: \: \: \: \: \: \: \: \: ( As \: \: log \: 10 = 1) }\\ \\ \bold{= 2}$

Answer 2

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$\: \: log 125+ log 216-3 log 30+log 100</p><p> \\ \\ = log \: 5 {}^{3} + log6 {}^{3} - 3 \: log \: (5 \times 6) + log \: 10 {}^{2} \\ \\ = 3 \: log \: 5 + 3 \: log \: 6 - 3 \: log \: 5 - 3 \: log \: 6 + 2 \: log \: 10 \\ \\ = 2 \: log \: 10 \\ \\ = 2$