Verified Answer :

olemakpadu

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

rdacoder

Answer: P = 10M

Step-by-step explanation:

We can rewrite the two equations as:

log P - log N = 5 .........(1)

log M - log N = 4 .........(2)

Subtracting equation (2) from equation (1) gives:

log P - log M = 1 ........(3)

Equation (3) can be written as:

\(log\frac{p}{m} =1\)

so,

\(10^1=\frac{p}{m}\)

simplify to

\(10=\frac{p}{m}\)

multiply both sides by m to get a final answer of

P = 10M

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