Thread: log help

State all solutions (a,b,c) for the system of equations a+b+c=2009 and log_a(b) = c^2009 where a,b,c are integers and a >= 2, b>= 1, c>=0. Explain your answer. Hint: First consider c.

hint doesn't really help me tbh.. just trying to solve some problems from last year's test and this is the only one i'm stuck on. any help regarding the approach would be appreciated

Consider the cases c = 0, c = 1 and c > 1.

ok, i got the solution is c=0, a=2008, b=1

and

c=1, a=1004, b=1004

am i right?

im also kind of confused for c=2, then log_ab=2^2009 so a^2^2009 = b, then what will b be? i know this won't be a solution but why?

oh nvm i guess it's because b is too large to satisfy the first equation