If log M/N=5 and log P/N=7, what can you say about the relationship between M and P?

Question

Answer 1

We need to use log rules here as well. We're going to use the fact that Log(a/b) = log(a) - log(b).

Log(M/N) = 5

This means that log(M) - log(N) = 5 . Let's call this Equation 1.

Log(P/N) = 7

This means that log(P) - log(N) = 7. Let's call this Equation 2.

If we take Equation 2 and Subtract Equation 1, this will allow us to eliminate Log(N).

log(M) - log(N) = 5

-log(P) + log(N) = -7

Log(M) - Log(P) = -2

Answer 2

If log is log base ten, then M/N = 10⁵ and P/N = 10⁷

Therefore P/M = 10² or P = 10²M

If you meant ln, then the relationship is P = e²M

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