Question

Using numerical analysis and the Quotient Rule of Logarithms, how can log(r^3/n^2)
be rewritten?(1 point)
Responses

3logr/2logn
Start Fraction 3 logarithm r over 2 logarithm n End Fraction

2logn−3logr
2 logarithm n minus 3 logarithm r

3logr−2logn
3 logarithm r minus 2 logarithm n

3logr+2logn

Answer 1

To rewrite \( \log\left(\frac{r^3}{n^2}\right) \) using the Quotient Rule of Logarithms, we apply the rule that states:

\[
\log\left(\frac{a}{b}\right) = \log(a) - \log(b)
\]

Applying this to \( \log\left(\frac{r^3}{n^2}\right) \):

1. Split the logarithm using the Quotient Rule:
\[
\log\left(\frac{r^3}{n^2}\right) = \log(r^3) - \log(n^2)
\]

2. Use the Power Rule of Logarithms, which states that \( \log(a^b) = b\log(a) \):
\[
\log(r^3) = 3\log(r) \quad \text{and} \quad \log(n^2) = 2\log(n)
\]

3. Substitute these results back into the equation:
\[
\log\left(\frac{r^3}{n^2}\right) = 3\log(r) - 2\log(n)
\]

Therefore, the expression can be rewritten as:

\[
3\log(r) - 2\log(n)
\]

So, the correct response is:

**3logr−2logn**