Using the properties of logarithms, convert the following: $$ \log _{6} x^{5} $$ $$ 5 \log 6 x $$ $$ 5 \log _{6} x $$ $$ \log 30 x $$ $$ 6 \log 5 x $$

Question

UpStudy AI · Accepted Answer

To convert the expression $$ \log_{6} x^{5} $$ using the properties of logarithms, we can apply the power rule, which states that $$ \log_{b} (a^{n}) = n \log_{b} a $$.

### Step 1: Apply the Power Rule
Using the power rule on $$ \log_{6} x^{5} $$:

$$
\log_{6} x^{5} = 5 \log_{6} x
$$

### Summary of Conversions
1. $$ \log_{6} x^{5} = 5 \log_{6} x $$
2. $$ 5 \log 6 x $$ is not a direct conversion of $$ \log_{6} x^{5} $$ but rather a different expression.
3. $$ 5 \log_{6} x $$ is the same as the result from step 1.
4. $$ \log 30 x $$ is not directly related to $$ \log_{6} x^{5} $$.
5. $$ 6 \log 5 x $$ is also not a direct conversion of $$ \log_{6} x^{5} $$.

### Final Result
The only valid conversion from the original expression $$ \log_{6} x^{5} $$ is:

$$
\log_{6} x^{5} = 5 \log_{6} x
$$
$$ \log_{6} x^{5} = 5 \log_{6} x $$

Using the properties of logarithms, convert the following: \( \log _{6} x^{5} \) \( 5 \log 6 x \) \( 5 \log _{6} x \) \( \log 30 x \) \( 6 \log 5 x \)

Solución de tutoría real

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Pre Algebra Questions