Why and how to the properties of logarithms work

In this video, Miss Mclogan explains the rules of logarithms, focusing on the addition of logarithms with the same base. She demonstrates this with an example using log base 2 of 4 and 32, showing how they multiply to log base 2 of 128. She then addresses a student's question about adding logarithms with different bases, illustrating the complications and why the same base is necessary for the rule to apply. The lesson concludes with a brief summary and final remarks.

How do you determine the base when combining logarithms?

What is the significance of having the same base in logarithmic operations?