Guys please help for precalculus ):

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Explanation:

Use the log rule

log(A/B) = log(A) - log(B)

this works for any valid log base

So we can say

meaning that

We have this system of equations

Subtract the equations straight down. You'll find the log(N) terms cancel out and we have the new equation log(P) - log(M) = 3 which transforms into log(P/M) = 3

Lastly, convert the log equation into its exponential equivalent form using the idea that log(b,x) = y  turns into y = b^x, where b is the base

Throughout this problem, the base wasn't given. Instead its implied we're talking about base 10.

So,

log(P/M) = 3

P/M = 10^3

P/M = 1000

P = 1000M

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Alternatively,

log(P/N) = 8 turns into P/N = 10^8

log(M/N) = 5 turns into M/N = 10^5

meaning that we can divide the two equations to get P/M = (10^8)/(10^5). That simplifies to P/M = 1000 and rearranges to P = 1000M