Cormen

Question

2n  is the order of 3n  . 

Is it True or False ? State with reason.

Comments

$2^n$  is order of $3^n$

does it mean :  $2^n$=O($3^n$) or $2^n$=o($3^n$)?

if it isO()..then it is false and if it is o() then true?

Answer 1

Say f(n)=2ⁿ and g(n)=3ⁿ

 f(n)=o(g(n))(small-oh) //////not tightest upperbound

so answer is false

Comments

yes, it should be. But "is the order of" is a bit ambiguous

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yes @Arjun Sir

thank u :)

log is not good here

because then both value will be equal to, rather than saying 3ⁿ asymptotically larger than 2ⁿ

If we get log2 and log3 then these are constant term , So, by this we cannot say one asymptotically larger than another

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yes. Because when we apply log we are changing the functions. i.e., $f(x)$ now becomes $g(f(x))$ where $g$ is the $\log$ function. Still this works for many functions and with some effort one can say for which all cases it won't work.