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In this video tutorial on logarithms, the concept of "cancelling out" in logarithmic equations is discussed. The goal is to determine what power the base needs to be raised to in order to result in the term within the brackets. For example, the log base 4 of 4 to the power of 8 simplifies to 8, as the base and number are the same, leaving only the exponent. This can be rewritten using the power rule as 8 log 4 of 4, revealing that 4 needs to be raised to the power of 1 to get 1.