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In this problem what we want to do is break the 2 numbers that we have down into terms of 2's and 3's only. So, lets start with 32 like shown, and we can take 32 and divide it by 2(which we need) and we get 16, so our first branch will be 2 and 16. Next, we can take 16 and break it up into 2 and 8, and we keep going 8 goes to 2and 4 and 4 goes into 2 and 2. When we are all done we end up with 5 2's. Now we need to break up 9. Since we cant break 9 into 2's anyway and we need 3's, the only thing we can do is break it up into 2 3's. And our final answer is written as, 5 log 2- 2 log 3.