Let log p/n=5 and log m/n=9 what is the relationship between p and m?

 we know that

log (P/N) = log P - log N
so
log P - log N = 5> equation 1

log (M/N) = log M - log N 
so
log M - log N = 9 > equation 2 

 If you subtract equation 2 from equation 1,
you have
log M - log P = 4  
That means that log (M/P) = 4 > 10^4 = M/P ---> M = 10000P

the answer is
the relationship between P and M is 
M = 10000P