Question
Expand the logarithm ln(13/x)
.(1 point)
Responses
ln 13 - ln x
ln 13 - ln x
ln(13 - x)
ln(13 - x)
ln 13ln x
ln 13ln x
13 - x
.(1 point)
Responses
ln 13 - ln x
ln 13 - ln x
ln(13 - x)
ln(13 - x)
ln 13ln x
ln 13ln x
13 - x
Answers
GPT-4o mini
The expansion of the logarithm \( \ln\left(\frac{13}{x}\right) \) can be done using the properties of logarithms, specifically the quotient rule:
\[
\ln\left(\frac{a}{b}\right) = \ln a - \ln b
\]
Applying this rule to \( \ln\left(\frac{13}{x}\right) \):
\[
\ln\left(\frac{13}{x}\right) = \ln 13 - \ln x
\]
So the correct answer is:
**ln 13 - ln x**
\[
\ln\left(\frac{a}{b}\right) = \ln a - \ln b
\]
Applying this rule to \( \ln\left(\frac{13}{x}\right) \):
\[
\ln\left(\frac{13}{x}\right) = \ln 13 - \ln x
\]
So the correct answer is:
**ln 13 - ln x**