Expand the logarithm ln(13/x)

Question

.(1 point)
Responses

ln 13/ln x
Start Fraction l n 13 over l n x End Fraction

13−x
13 minus x

ln(13−x)
l n left parenthesis 13 minus x right parenthesis

ln 13−ln x

Answer 1

To expand the logarithm \( \ln\left(\frac{13}{x}\right) \), you can use the property of logarithms that states:

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

Applying this to your expression:

\[ \ln\left(\frac{13}{x}\right) = \ln(13) - \ln(x) \]

So, the correct response from your options is:

\[ \ln 13 - \ln x \]