Which of the following rewritten logarithms uses the Power Rule of Logarithms to evaluate log $$ 8^{\frac{3}{4}} $$ $$ \frac{3}{4} \log 8 $$ $$ -\frac{4}{3} \log 8 $$ $$ -\frac{3}{4} \log 8 $$ $$ \frac{4}{3} \log 8 $$

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UpStudy AI · Accepted Answer

To evaluate $$ \log 8^{\frac{3}{4}} $$ using the Power Rule of Logarithms, we apply the rule which states that $$ \log a^b = b \log a $$.

Here, we have:

- $$ a = 8 $$
- $$ b = \frac{3}{4} $$

Applying the Power Rule:

$$
\log 8^{\frac{3}{4}} = \frac{3}{4} \log 8
$$

Now, let's analyze the options provided:

1. $$ \frac{3}{4} \log 8 $$ - This matches our result.
2. $$ -\frac{4}{3} \log 8 $$ - This does not match.
3. $$ -\frac{3}{4} \log 8 $$ - This does not match.
4. $$ \frac{4}{3} \log 8 $$ - This does not match.

Thus, the correct rewritten logarithm that uses the Power Rule of Logarithms to evaluate $$ \log 8^{\frac{3}{4}} $$ is:

$$
\frac{3}{4} \log 8
$$
The correct rewritten logarithm is $$ \frac{3}{4} \log 8 $$.

Which of the following rewritten logarithms uses the Power Rule of Logarithms to evaluate log \( 8^{\frac{3}{4}} \) \( \frac{3}{4} \log 8 \) \( -\frac{4}{3} \log 8 \) \( -\frac{3}{4} \log 8 \) \( \frac{4}{3} \log 8 \)

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