LOGARITHMS B21

Evaluate Log₅(125 x 625).

Solution

= Log₅(125 x 625)

= Log₅125 +  Log₅625          (applying the product rule)

= Log₅5³ +  Log₅5⁴             ( 125= 5³ and 625=5⁴ by prime factorization)

= 3Log₅5 +  4Log₅5       ( remember  Log_aa^c = cLog_aa )

= (3 x 1) +  (4 x 1)          ( remember  Log_aa = 1 )

= 3 + 4

= 7

Hence Log₃(125 x 625) = 7

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

Evaluate Log₅(15625 x 625).