Using numerical analysis and the Quotient Rule of Logarithms, how can lnm−ln44

ln

𝑚

ln

44
be rewritten?(1 point)
Responses

ln(44m)
ln

(
44
𝑚
)
the natural log of open paren 44 over m close paren

ln(m44)
ln

(
𝑚
44
)
the natural log of open paren m over 44 close paren

lnmln44
ln

𝑚
ln

44
lnmln44
ln

𝑚
ln

44

ln(m−44)

1 answer

To rewrite the expression \( \ln m - \ln 44 \) using the Quotient Rule of Logarithms, you can use the rule which states:

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

Applying this to \( \ln m - \ln 44 \):

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

So the correct response is:

The natural log of open paren m over 44 close paren, or \(\ln\left(\frac{m}{44}\right)\).

This option is not explicitly listed in your responses, but it is the accurate rewrite of the expression. If you had to choose from the given options, "the natural log of open paren 44 over m close paren" would be incorrect, as that would represent -\( \ln\left( \frac{44}{m} \right) \).