LOGARITHMS 8

Evaluate Log₂(2048 x 32).

Solution

= Log₂(2048 x 32)

= Log₂2048 +  Log₂32          (applying the product rule)

= Log₂2¹¹ +  Log₂2⁵             ( 2048= 2¹¹ and 32=2⁵ by prime factorization)

= 11Log₂2 +  5Log₂2       ( remember  Log_aa^c = cLog_aa )

= (11 x 1) +  (5 x 1)          ( remember  Log_aa = 1 )

= 11 + 5

= 16

hence Log₂(1048 x 32) = 12 

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

Evaluate Log₂(256 x 512).