Question

Help me out here please! Thanks.

Answer 1

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

Explanation:

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

The log of a product is the sum of the logs.

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

Now, write the root as a rational power.

`= \log_3 x^(1)/(5) + \log_3 y`

The log of a power is the the exponent times the log of the base.

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

Answer 2

A.
`(1)/(5) log_(3)x +log_(3)y`

Explanation:

We have the expression

`log_(3) (\sqrt[5]{x} *y)`

As these two values are being multiplied, we can separate the two and the sum of them will be equal to the multiplied version

`log_(3)\sqrt[5]{x} +log_(3)y`

The
`\sqrt[5]{x}` can be rewritten as
`x^{(1)/(5) }`. This allows us to use the exponent rule. This means that it can be written as

`(1)/(5) log_(3)x +log_(3)y`