This is one of the most vital sections for logarithms. We cover primary and secondary properties of logs, which are pivotal in future math classes as these properties are often exploited in otherwise difficult mechanical situations.
The previous examples work nicely as long as we have logs with matching bases. In the unfortunate (but likely) situation where the bases don’t match, we will need a way to manipulate the bases so that we can use our above properties. This leads us to the ‘change of base’ formula for logarithms.
If we generalize the previous example, we can actually derive the fully generalized change of base formula. If you want to change the base from to the base , then you can use the following equation;