Let's prove the following theorem:

log_b(b^p) = p

Additional Assumptions

1	log_b(b^p) = m

Proof Table

#	Claim	Reason
1	b^m = b^p	if log_b(b^p) = m, then b^m = b^p (Converse of Log Definition)
2	m = p	if b^m = b^p, then m = p (Converse of Power Substitution)
3	log_b(b^p) = p	if log_b(b^p) = m and m = p, then log_b(b^p) = p (Transitive Property of Equality)

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