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Vlada [557]
3 years ago
9

Help me out here please! Thanks.

Mathematics
2 answers:
Setler79 [48]3 years ago
4 0

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

leva [86]3 years ago
3 0

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

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