Question

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 1

Answer:

$L(x)=\frac{\ln(72)}{\ln(8)}$

Explanation:

Given the logarithmic expression:

$\log_872$

We want to rewrite it in terms of natural logarithms using the change-of-base theorem.

The change of base formula is given below:

$\begin{equation}\log _{b}(a)=\frac{\log _{x}(a)}{\log _{x}(b)}\end{equation}$

Let the new base be x=e, a=72, and b=8.

$\begin{gathered} \log_872=\frac{\log_e(72)}{\log_e(8)} \\ \implies L(x)=\frac{\ln(72)}{\ln(8)} \end{gathered}$

The formula in a natural logarithm form can be written as:

$L(x)=\frac{\ln(72)}{\ln(8)}$