Respuesta :

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]

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