Question

Question
Using numerical analysis and the Quotient Rule of Logarithms, how can log(r3n2)
be rewritten?(1 point)
Responses

3logr2logn
Start Fraction 3 logarithm r over 2 logarithm n End Fraction

3logr+2logn
3 logarithm r plus 2 logarithm n

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

2logn−3logr

Answer 1

To rewrite \( \log(r^3 n^2) \) using the properties of logarithms, we can apply the product and power rules.

The logarithm of a product can be expressed as the sum of the logarithms:

\[
\log(a \cdot b) = \log(a) + \log(b)
\]

And the power rule applies as follows:

\[
\log(a^b) = b \cdot \log(a)
\]

Now, applying these rules to \( \log(r^3 n^2) \):

1. Start with the expression:
\[
\log(r^3 n^2)
\]

2. Use the product rule:
\[
= \log(r^3) + \log(n^2)
\]

3. Apply the power rule:
\[
= 3\log(r) + 2\log(n)
\]

So, the final rewritten form of \( \log(r^3 n^2) \) is:

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

Therefore, the correct response is:

**3logr + 2logn**