Question

Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)

Answer 1

`log_3((21)/(5)) = log_3(7) - log_3(5)+ 1`

Explanation:

Given

`log_3((21)/(5))`

Required

Express in terms of
`log_3(5)` and
`log_3(7)`

`log_3((21)/(5))`

Express 21 as 7 * 3

`log_3((21)/(5)) = log_3((7 * 3)/(5))`

Apply law of logarithm

`log_3((21)/(5)) = log_3(7) + log_3(3) - log_3(5)`

`log_3(3) = 1`. So, we have:

`log_3((21)/(5)) = log_3(7) + 1 - log_3(5)`

Rewrite:

`log_3((21)/(5)) = log_3(7) - log_3(5)+ 1`