LOGARITHMS 2

Evaluate Log₂(256 x ¹/₃₂).

Solution

= Log₂(256  x ¹/₃₂).

= Log₂256 +  Log₂(¹/₃₂)          (applying the product rule)

= Log₂256 +  Log₂32^-1         ( since  ¹/₃₂ = 32^-1 )

= Log₂2⁸ +  Log₂(2⁵) ^-1                      ( since 256= 2⁸ and 32=2⁵ )

= Log₂2⁸ +  Log₂2^-5   

= 8Log₂2 +  -5Log₂2       ( remember  Log_aa^c = cLog_aa )

= (8 x 1) +  (-5 x 1)          ( remember  Log_aa = 1 )

= 8 + (-5)

= 3

Hence Log₂(256 x ¹/₃₂) = 3

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

Evaluate Log₂(512 x ¹/₁₂₈).