Currently, in my math class, we are learning about logarithms. I understand that the common logarithm has a base of 10 and the natural has a base of e. But, when do we use them?
For example the equation $7^{x-2} = 30$
in the lesson, you solve by rewriting the equation in logarithmic form $\log_7 30 = x-2$. The,n apply the change of base formula, and use a calculator to evaluate.
$$\frac{\ln30}{\ln7}$$
now this is where I get confused. Why do use natural logarithms here? Why don't we use common logarithms? Am I missing something simple?
Any help is greatly appreciated.
Best Answer
The point of making a change of base is that your calculator probably doesn't have a button to evaluate logarithms with an arbitrary base, but it does have a button to evaluate natural logarithms. So the only thing special about $e$ here is that your calculator knows how to compute logarithms in base $e$. If your calculator happens to also have a button for logarithms in base $10$, it would be perfectly fine to use them instead.