Question

Help with logs

Answer 1

\( \log \dfrac{M}{N} = 4\) Eq. (1)

\( \log \dfrac{P}{N} = 7\) Eq. (2)

From Eq. (1) we get:

\( \log M - \log N = 4\)

\( -\log N = 4 - \log M\) Eq. (3)

From Eq. (2) we get:

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

\(- \log N = 7 - \log P\) Eq. (4)

Equate equations (3) and (4) to get

\(4 - \log M = 7 - \log P \)

\(\log P - \log M = 7 - 4\)

\(\log \dfrac{P}{M} = 3\)

Use the definition of log to wriite:

\(10^3 = \dfrac{P}{M} \)

\( P = 1000 M\)

Answer 2

thank you! @mathstudent55

Answer 3

You're welcome.