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in this video were briefly going to go over some properties of logs that you need to be familiar with the first one is the power rule lets say we have log a raised to the n you can move the exponent in front so this is equal to n log a the second is the product rule log a times log b is equal to log a plus log b and then you have the quotient rule log a divided by log b is log a minus log b so we can use this in order to evaluate logs so for instance lets say if we want to simplify log base 5 of 5 raised to the 7. so what we can do is move the seven to the front so this is equal to seven log base five of five a log base five of five because theyre the same its equal to one and 7 times 1 is 7. lets try another example like that log base 2 of 8 raised to the fifth power so lets move the 5 to the front so this is equal to 5 times log base 2 of 8. now how many twos do we need to multiply to get to 8 we need to multiply 3 2s 2 to the third is 8 so log base two of a is three and five