LOGARITHMS B22

Evaluate Log₂(64 x 256).

Solution

= Log₂(64 x 256)

= Log₂64 +  Log₂256          (applying the product rule)

= Log₂2⁶ +  Log₂2⁸             ( 64= 2⁶ and 256=2⁸ by prime factorization)

= 6Log₂2 +  8Log₂2       ( remember  Log_aa^c = cLog_aa )

= (6 x 1) +  (8 x 1)          ( remember  Log_aa = 1 )

= 6 + 8

= 14

Hence Log₂(64 x 256) = 18

TRY THIS.......

Evaluate Log₂(2048 x 256).