Answer:
C. P= 1000M
Step-by-step explanation:
[tex]log(\frac{M}{N} )=4[/tex]
Using the quotient rule of logs we can write:
log(M) - log(N) = 4
or
log(M) - 4 = log(N) (Equation 1)
[tex]log(\frac{P}{N} )=4[/tex]
Using the quotient rule of logs we can write:
log(P) - log(N) = 7
or
log(P) - 7 = log(N) (Equation 2)
Comparing equation 1 and 2, we can write:
log(M) - 4 = log(P) - 7
-4 + 7 = log(P) - log(M)
log(P) - log(M) = 3
[tex]log(\frac{P}{M} )=3[/tex]
Converting the log to exponential form we get:
[tex]\frac{P}{M}=10^{3}\\\\\frac{P}{M}=1000\\\\P=1000M[/tex]
Thus, option C gives the correct answer.
