Fill in the missing values to make the equations true.

Question

a) log8 11+log8 5=log 8 _

b) log3 11-log3 _=log3 11/4

c) log7 25=2log7 _

Answer 1

Hi Aubree

Each of these problems involves using the properties of logarithms

a) log8 11+log8 5=log 8 _

b) log3 11-log3 _=log3 11/4

c) log7 25=2log7 _

Log Product Rule: log_bmn = log_bm + log_bn

Log Quotient Rule: log_bm/n = log_bm - log_bn

Power Rule: log_bm^p = p log_bm

a) log₈11+log₈5=log₈(11 x 5)

= log₈55 (log product rule)

b) log₃11-log₃ _=log₃(11/4)

log₃(11/4) = log₃11 - log₃4 (log quotient rule)

c) log₇25=2log₇_ 25 is 5²

log₇5² = 2log₇5 (Log power rule)

Hope this helps.

Let me know if you need further clarification :)