Use the properties of logarithms to write the following logarithm in terms of log7(2) and log7(3). log7(14/3)

Answer 1

Use the properties of logarithms to write the following logarithm in terms of log7(2) and log7(3). log7(14/3)

log₇ (14/3) = log₇14 - log₇3 = log₇ (7*2) - log₇3 = log₇7 + log₇2 - log₇3 = 1+ log₇2 - log₇3

Explanation:

1. when you have division inside of a logarithm, it equals to dividing logarithms log(a/b)= log(a) - log(b)
2. when you have multiplication inside of a logarithm, it equals to adding logarithms log (a*b)= log(a) + log(b)
3. log_a(a)=1