LOGARITHMS B16

Evaluate Log₃(9 x 243).

Solution

= Log₃(9 x 243)

= Log₃9 +  Log₃243        (applying the product rule)

= Log₃3² +  Log₃3⁵    ( 9= 3² and 243=3⁵ by prime factorization)

= 2Log₃3 +  5Log₃3      ( remember  Log_aa^c = cLog_aa )

= (2 x 1) +  (5 x 1)        ( remember  Log_aa = 1 )

= 2 + 5

= 7

Hence Log₃(9 x 243) = 7.

TRY THIS........

Evaluate Log₃(9 x 729).