Induction proof involving log(m+1) terms

[seeker101]

Any suggestions on how to simplify the log (m+1) terms that arise when proving the following statement using induction for m >= 1? (log to the base 2)

[PLAIN]http://dl.dropbox.com/u/471735/recurrence%202.png

 

[Petr Mugver]

You don't need to use induction, because there is a straightforward method: note that log(m/2) = log(m) - 1 so your disequation becomes simply log(m) > 1 which is obvious for m > 1.