Question

How would you write this expression as a sum or difference?

Answer 1

A.
`(1)/(5) log_3(x) + log_3(y)`

Explanation:

Log rules tell us that multiplication inside a log can be expressed as two summands with the same base.
In other words:

`\log_c(a*b) =\log_c(a)+\log_c(b)`

In this case:

`log_3(\sqrt[5]{x} * y) = log_3(\sqrt[5]{x}) + log_3(y)`

Using log exponent rules(power can be moved to the front of a log), we get our final answer:

`(1)/(5) log_3(x) + log_3(y)`