How is log 72 written in terms of natural logarithms using the change-of-base theorem?The formula log 72 in a natural logarithm can be written as L(x) = -

Answer:
[tex]L(x)=\frac{\ln(72)}{\ln(8)}[/tex]Explanation:
Given the logarithmic expression:
[tex]\log_872[/tex]We want to rewrite it in terms of natural logarithms using the change-of-base theorem.
The change of base formula is given below:
[tex]\begin{equation}\log _{b}(a)=\frac{\log _{x}(a)}{\log _{x}(b)}\end{equation}[/tex]Let the new base be x=e, a=72, and b=8.
[tex]\begin{gathered} \log_872=\frac{\log_e(72)}{\log_e(8)} \\ \implies L(x)=\frac{\ln(72)}{\ln(8)} \end{gathered}[/tex]The formula in a natural logarithm form can be written as:
[tex]L(x)=\frac{\ln(72)}{\ln(8)}[/tex]