Hello student,
Logarithm can be a bit confusing if you are not well versed with its properties. It is not possible to list here all the important properties and concepts, so for an in-depth you can visit the website. However, I am listing here some of the concepts and examples and hope they help in clearing your doubts to some extent:
The relations a^x = N and log_aN = x are identical where N > 0, a > 0, a is not 1.
Hnece, logarithm of anumbe to some base is the exponent by which the base must be rasied in order to get that number.
There is no set rule to be followed for qeustions on logarithm. Once you are well versed with the properties and practice agood number of questions, you can master this topic.
Eg 1:

Now,in this question we have just simplified using the properties of logarithm.
Base changing theorem is also important and let’s have one question based on that too:
Eg 2:
We have utilized various properties here like
1/(log_ab) = log_ba and log_ba = log_ca/log_cb.