Question
Expand the logarithm ln(13x)
.(1 point)
Responses
ln13lnx
Start Fraction l n 13 over l n x End Fraction
ln13−lnx
l n 13 minus l n x
13−x
13 minus x
ln(13−x)
.(1 point)
Responses
ln13lnx
Start Fraction l n 13 over l n x End Fraction
ln13−lnx
l n 13 minus l n x
13−x
13 minus x
ln(13−x)
Answers
GPT-4o mini
To expand the logarithm \( \ln(13x) \), you can use the property of logarithms that states \( \ln(ab) = \ln(a) + \ln(b) \).
Applying this property, we have:
\[
\ln(13x) = \ln(13) + \ln(x)
\]
Thus, the correct option from your provided responses is not explicitly listed. However, if we consider the individual components:
- The expansion does not yield \( \ln 13 \ln x \), \( \frac{\ln 13}{\ln x} \), \( 13 - x \), or \( \ln(13 - x) \).
As a result, the answer is:
\[
\ln(13) + \ln(x)
\]
If you have to choose from given options, the closest relevant transformation is \( \ln 13 - \ln x \), but that also is incorrect for the context of the expansion. Make sure to look for the combination \( \ln(13) + \ln(x) \) as the proper log expansion.
Applying this property, we have:
\[
\ln(13x) = \ln(13) + \ln(x)
\]
Thus, the correct option from your provided responses is not explicitly listed. However, if we consider the individual components:
- The expansion does not yield \( \ln 13 \ln x \), \( \frac{\ln 13}{\ln x} \), \( 13 - x \), or \( \ln(13 - x) \).
As a result, the answer is:
\[
\ln(13) + \ln(x)
\]
If you have to choose from given options, the closest relevant transformation is \( \ln 13 - \ln x \), but that also is incorrect for the context of the expansion. Make sure to look for the combination \( \ln(13) + \ln(x) \) as the proper log expansion.