In order to use the power rule of logs correctly, you need to be careful with what is the base of a particular exponent and what is not part of the base. The power moves out front of only the log (or logs) that have the base. Most errors come when the power is moved out front of multiple logs that should not, in fact, have that power applied. If you're in doubt, expand all of the products to sums first, and then go back and move the powers out front.
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