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in this lesson were going to take a single log and expand it into a sum or difference of logs so before we do that lets just review some basic properties as you mentioned before log of a to the n is equivalent to n log a and log a times b you can expand it as log a plus log b and log a divided by b is going to be log a minus log b now because a is on the top its going to have a positive sign next to it b is on the bottom so it has a negative sign next to it so consider this problem log x y divided by z go ahead and expand the expression x and y are both on top so its going to be positive log x plus log y z is on the bottom so its going to be minus log z try this one log a squared b to the third c to the fourth d to the fifth go ahead and expand it so a and b are both on top so its going to be positive log a squared plus log b to the third c and d are on the bottom so its going to have a negative sign in front of it so its going to be minus log c to the fourth minus log d to th
