1. ## Induction Proof Help

5^n + 9 < 6^n for all integers n>=2.

Base Case: 5^(2) + 9 < 6^(2)
34<36
Assume P(k) true: 5^k + 9 < 6^k

P(k+1): 5^(k+1) + 9 < 6^(k+1)

How do I complete the proof? If 5 and 6 were the same base I could understand multiplying to the common base to achieve the ^k+1, but the different bases really have thrown me off!

2. $6^{k+1} = 6 \cdot 6^k > 6 \cdot (5^k + 9) \dots$