LOGARITHMS B20

Evaluate Log₅(25 x 625).

Solution

= Log₅(25 x 625)

= Log₅25 +  Log₅625          (applying the product rule)

= Log₅5² +  Log₅5⁴             ( 25= 5² and 625=5⁴ by prime factorization)

= 2Log₅5 +  4Log₅5       ( remember  Log_aa^c = cLog_aa )

= (2 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 2 + 4

= 6

Hence Log₃(25 x 625) = 6

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

Evaluate Log₅(25 x 15625).