LOGARITHMS B17

Evaluate Log₃(729 x 243).

Solution

= Log₃(729 x 243)

= Log₃729 +  Log₃243          (applying the product rule)

= Log₃3⁶ +  Log₃3⁵    ( 729= 3⁶ and 243=3⁵ by prime factorization)

= 6Log₃3 +  5Log₃3       ( remember  Log_aa^c = cLog_aa )

= (6 x 1) +  (5 x 1)          ( remember  Log_aa = 1 )

= 6 + 5

= 11

Hence Log₃(729 x 243) = 11

TRY THIS........

Evaluate Log₃(729 x 9).