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so say you have log base B of X times y if you expand this you get log base B of X plus log base B of Y so when you multiply these are called the arguments when theyre multiplied you can write it as the sum of two logs you just want to make sure you keep the same base whatever this base is space 3 these will both be base 3 its base 10 the both be base 10 log base B of X divided by Y what do we do when we divide we can expand this by subtracting the two logs okay so when you divide you take a log of the numerator minus log of the denominator so log of the one on top - log of the one on the bottom again keeping the same base and then the power property for logs okay you have this power okay up here this exponent you can bring that down in front as a coefficient so we could write this as n log base B of X so this is called the product property product means multiply you write it as a sum quotient property youre dividing you write it as a difference and power property bring down that po