Question

Write the expression as a single logarithm.

log₄ 2x - log₄ 6y

Answer 1

`log_(4)((2x)/(6y))`

Explanation:

According to the Quotient Rule (Logarithmic Property):

`log_(a)x - log_(a)y = log_(a)((x)/(y))`

Therefore, you could combine the logarithmic expressions as:

`log_(4)2x - log_(4)6y = log_(4)((2x)/(6y))`

Optional:

If ever you're required to simplify it further,
`log_(4)((2x)/(6y))` will be:

`log_(4)((2x)/(6y)) = log_(4)((x)/(3y))`