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Hi! I need help with a practice problem. Im not quite sure how to solve it....

Hi! I need help with a practice problem. Im not quite sure how to solve it. Thank you in advance!

Let f(n) = log3n + 1. Prove f(n) is O(log19n). Hint: Use the change of base formula for logs.

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Answer #1

log19(n) = log3(n) / log3(19)

=> log3(n) =  2.68 * log19(n)

Hence, for c = 3.68 and n = 0, we have

0 <= log3n + 1 <= 3.68 * log19(n)

Hence, f(n) = O(log19 n)

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