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Your friend proposes a new divide-and-conquer algorithm for sorting your music in order of awesomeness. In each step, the algorithm splits the problem into 8 subproblems all at once, but with a split cost of for a problem of size . The base case costs . We can model this with a recursive defintiion. The base case is . The recursive formula is . Assuming that is a power of 8, how long will the algorithm take

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