Use the properties of logarithms to write the logarithm in terms of log 7 (3) and log 7 (5)

Question

Use the properties of logarithms to write the logarithm in terms of log 7 (3) and log 7 (5)

log 7(147/25)

Answer 1

log₇(147/25)

= log₇(3*7*7/5*5)

= log₇(3*7*7) - log₇(5*5)

= (log₇3 + log₇7 + log₇7) - (log₇5 + log₇5)

= (log₇3 + 1 + 1) - 2*log₇5

= 2 + log₇3 - 2*log₇5