Natural Logarithms

The Natural Logarithms are very similar to the common logarithms, the difference is that you have a base e that is constant. The natural logarithm is the logarithm to the base e, where e is an irrational constant approximately equal to 2.718281828. The natural logarithm is generally written as ln(x), log_e(x). The natural logarithm of a number is the power to which e would have to be raised to equal to that number. For example; the In(54.59815…) is 4 because e⁴ is equal 54.59815… You might get a function like the following;

You can turn this function into a function involving logs, to do so you simply take each side of the function to a log with base e. You just simply add the log_e at the beginning of each side as below as then you’ll be able to find the logarithm.

Use the rules of logs to convert one of the sides with log_ee^x using the logs rules to give you;

Now simplify, You know that;

…according to the logs rules. That leaves you with;

which is the same as;

In general we say that;

The rules of logs also apply to natural logs as you will realise below;

Natural logs rules