LOGARITHMS B13

Evaluate Log₂(1024 x 16).

Solution

= Log₂(1024 x 16)

= Log₂1024 +  Log₂16          (applying the product rule)

= Log₂2¹⁰ +  Log₂2⁴   ( 1024= 2¹⁰ and 16=2⁴ by prime factorization)

= 10Log₂2 +  4Log₂2       ( remember  Log_aa^c = cLog_aa )

= (10 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 10 + 4

= 14

hence Log₂(4 x 16) = 14

TRY THIS.......

Evaluate Log₂(1024 x 128).