LOGARITHMS B15

Evaluate Log₂(1024 x 256).

Solution

= Log₂(1024 x 256)

= Log₂1024 +  Log₂256          (applying the product rule)

= Log₂2¹⁰ +  Log₂2⁸       ( 1024= 2¹⁰ and 256=2⁸ by prime factorization)

= 10Log₂2 +  8Log₂2       ( remember  Log_aa^c = cLog_aa )

= (10 x 1) +  (8 x 1)          ( remember  Log_aa = 1 )

= 10 + 8

= 18

hence Log₂(1024 x 256) = 18

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

Evaluate Log₃(729 x 243).