If log (m/n) = 4 and log (p/n) = 5 what is the relationship between m and p? p=100m p=10m p=0.1m m=10p

Log (A/B) = logA - logB By law of logarithm

log (m/n) = 4

logm - logn = 4 ... (a)

log (p/n) = 5

logp - logn = 5 ... (b)

Equation (a) minus (b)

logm - logp - logn - (-logn) = 5 - 4

logm - logp - logn + logn = 1

logm - logp = 1

log (m/p) = 1

log₁₀ (m/p) = 1.

All the while the logarithm has been to base 10. Once a base is not written in logarithm, it is taken to be base 10.

log₁₀ (m/p) = 1

(m/p) = 10¹ conversion from logarithm to indices

m/p = 10

m = 10p