LOGARITHMS B18

Evaluate Log₃(729 x 81).

Solution

= Log₃(729 x 81)

= Log₃729 +  Log₃81          (applying the product rule)

= Log₃3⁶ +  Log₃3⁴     ( 729= 3⁶ and 81=3⁴ by prime factorization)

= 6Log₃3 +  4Log₃3       ( remember  Log_aa^c = cLog_aa )

= (6 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 6 + 4

= 10

Hence Log₃(729 x 243) = 10

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

Evaluate Log₃(6561 x 81).