Question

Guys please help for precalculus ):

Answer 1

Answer: Choice A. P = 1000M

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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

• log(P/N) = log(P) - log(N)
• log(M/N) = log(M) - log(N)

meaning that

• log(P/N) = 8 turns into log(P) - log(N) = 8
• log(M/N) = 5 turns into log(M) - log(N) = 5

We have this system of equations

$\begin{cases}\log(P)-\log(N) = 8\\ \log(M)-\log(N) = 5\end{cases}$

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