Question

Using numerical analysis and the Quotient Rule of Logarithms, how can lnm−ln44
be rewritten?(1 point)
Responses

ln(44m)
l n left parenthesis Start Fraction 44 over m End Fraction right parenthesis

lnmln44
Start Fraction l n m over l n 44 End Fraction

ln(m−44)
l n left parenthesis m minus 44 right parenthesis

ln(m44)

Answer 1

To rewrite \( \ln m - \ln 44 \) using the Quotient Rule of Logarithms, we can apply the rule which states that:

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

In this case, \( a = m \) and \( b = 44 \). Therefore, we can rewrite \( \ln m - \ln 44 \) as:

\[
\ln\left(\frac{m}{44}\right)
\]

Looking at the provided options, this corresponds to:

\(\ln\left(\frac{44}{m}\right)\) would actually be the reciprocal of what we've simplified.

The response that matches is:
\[
\ln\left(\frac{m}{44}\right)
\]

However, since that was not listed, it seems that the closest provided choice based on the Quotient Rule should correctly be:

\[
\ln\left(\frac{m}{44}\right)
\]

None of the provided choices exactly match this, but \( \ln\left(\frac{44}{m}\right) \) also follows from the original equation by flipping that ratio. Therefore, if the provided options are taken literally, none are correct.

Thus, the best interpretation here is:

\[
\ln\left(\frac{m}{44}\right)
\] is potentially what you are searching for, but please verify if there is an error in the choices given.