LOGARITHMS B19

Evaluate Log₃(729 x 27).

Solution

= Log₃(729 x 27)

= Log₃729 +  Log₃27          (applying the product rule)

= Log₃3⁶ +  Log₃3³             ( 729= 3⁶ and 27=3³ by prime factorization)

= 6Log₃3 +  3Log₃3       ( remember  Log_aa^c = cLog_aa )

= (6 x 1) +  (3 x 1)          ( remember  Log_aa = 1 )

= 6 + 3

= 9

Hence Log₃(729 x 27) = 9

TRY THIS.................

Evaluate Log₃(729 x 6561).