Question

If log(m/n) = 4 and log(p/n) = 5 what is the relationship between m and p? p=100m p=10m p=0.1m m=10p

Answer 1

Answer: P = 10M

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(p)/(m) =1`

so,

`10^1=(p)/(m)`

simplify to

`10=(p)/(m)`

multiply both sides by m to get a final answer of

P = 10M

Answer 2

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