Use the logarithm power law without shrinking the real domain
Problem
Expand \(\log_b(x^5)\) using the power law and state its maximal real domain.
Big Picture
What this problem is really about
The power law moves an exponent outside as a multiplier, but domain analysis comes first. Determine when the original powered argument is positive, paying attention to whether the power preserves or changes the sign of its base. Then make sure the logarithm left after expansion exists on the same inputs.
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