Question

Help me out here please! Thanks.

Answer 1

Answer:

A. $\frac{1}{5} log_{3}x +log_{3}y$

Step-by-step 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 $x^{\frac{1}{5} }$. This allows us to use the exponent rule. This means that it can be written as

$\frac{1}{5} log_{3}x +log_{3}y$

Answer 2

Answer:

A. $\dfrac{1}{5} \log_3 x + \log_3 y$

Step-by-step 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.

$= \log_3 x^\frac{1}{5} + \log_3 y$

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

$= \dfrac{1}{5} \log_3 x + \log_3 y$