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all right um so what we have here is we have log base 4 of 2 plus log base 4 of 32 so to solve this type of problem what were going to have to do is um were going to have to see see if we can evaluate the logarithms but you know the problem says not to use a calculator so its fun right um so 4 raised to what number is going to give me 2. well thats kind of a tough one because 4 raised to the first power gives me 4. um 4 to the one-half power that would give me 2. so i can actually do you know 4 to the one-half power would work and however were going to get a little bit trickier here so here so this would be one half good i got that but then log base 4 32 so 4 to square is 16 4 cubed though is 64. so theres not going to be an even number thats going to give me 32 right well so i guess i could probably maybe see if i can think about real hard in my head but otherwise i see i have an addition problem well i know i can use my propertys logarithm to condense it down to one logarith