LOGARITHMS B5

 

Evaluate Log₂(1024 x 64 x 256).

 

Solution

 

= Log₂(1024 x 64 x 256)

 

= Log₂1024 +  Log₂64 +  Log₂256         (applying the product rule)

 

= Log₂2¹⁰+  Log₂2⁶    +  Log₂2⁸           (Since1024= 2¹⁰, 64=2⁶ ,32=2⁵)

 

= 10Log₂2 +  6Log₂2    +  8Log₂2         ( remember  Log_aa^c = cLog_aa )

 

= (10 x 1) +  (6 x 1) +  (8 x 1)                  ( remember  Log_aa = 1 )

 

= 10 + 6 + 8

 

= 24 answer

 

 

hence Log₂(1024 x 64 x 256) = 22

 

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

 

Evaluate Log₂(512 x 128 x 1024).