Question

Logarithm please help

Answer 1

Given ;

LHS :

• 1/2 log9 + 2log6 + 1/4log81 - log12

using the property of log : nlogm = logmⁿ

• log√9 + log6² + log ⁴√81 - log12
• log3 + log36 + log3 - log12

using the property of log :

• logm + logn = log(mn)
• logm - logn = log(m/n)

Thus

• log(3×3×36) - log12
• log(3²×36/12)
• log(3²×3)
• log(3³)

using the property of log : nlogm = logmⁿ

• 3log3 = RHS

Hence proved.

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