Answered step by step
Verified Expert Solution
Question
1 Approved Answer
Facts: 1 . log ( ab ) = loga + logb 2 . log ( ac ) = cloga 3 . loga = log a
Facts:
logablogalogb
logaccloga
loga log a logb b
blogb a a Answer the following::
Question
a Using induction and fact prove fact for positive integers c
b Use fact and fact to show that log ab logalogb
c It is often said that the bases of logarithms do not matter when finding asymptotic bounds, although this idea is sometimes used too freely. To understand when we can ignore base, use fact to show that loga n Theta logb n for any positive a b
d A common mistake some students make is claiming that clogb n Theta n Sometimes, they claim this function is exponential. Give a counterexample for both claims find a positive c and b in which clogb n is neither exponential in n nor linear in n
e Complete the argument above by showing that for all positive c and b clogb n Theta nk for some k this implies that such functions are never exponential in n but the base does matter! Your argument should use facts and
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started