LOGARITHMS B22

Evaluate Log₅(3125 x 625).

Solution

= Log₅(3125 x 625)

= Log₅3125 +  Log₅625          (applying the product rule)

= Log₅5⁵ +  Log₅5⁴   ( 3125= 5⁵ and 625=5⁴ by prime factorization)

= 5Log₅5 +  4Log₅5       ( remember  Log_aa^c = cLog_aa )

= (5 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 5 + 4

= 9

Hence Log₃(1325 x 625) = 9.

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

Evaluate Log₅(3125 x 15625).