LOGARITHMS 9

Simplify Log₂1024 – Log₅3125 – Log₆216.

Solution

= Log₂1024 – Log₅3125 – Log₆216

= Log₂2¹⁰ – Log₅5⁵ – Log₆6³

= 10Log₂2 – 5Log₅5 – 3Log₆6  because Log_aaⁿ =  nLog_aa

= (10 x 1) – (5 x 1) – (3 x 1)    

= 10 – 5 – 3

= 10 – 8     [since -5 - 3 = -8]

= 2

Hence Log₂1024 – Log₅3125 – Log₆216= 2 

TRY THIS…………..

Simplify Log₂4096 – Log₃81 – Log₅3125