Question

Write the expression
5In M+ 3In N -2IN P - In R as a single logarithm.
If someone could start for me or walk me through it, I'd appreciate it..

Answer 1

Start with these rules:
\[a \ln b=\ln b^a\]
\[\ln (ab)=\ln a + \ln b\]
\[\ln \frac{ a }{ b }=\ln a - \ln b\]

Basically the coefficients become exponents on the part after the corresponding log. When you combine added logs go in the numerator, and subtracted ones go in the denominator.

An example:

\[3 \ln x + 4 \ln y - 5 \ln z\]
\[=\ln x^3 + \ln y^4 - \ln z^5\]
\[=\ln \frac{ x^3y^4 }{ z^5 }\]

Answer 2

\[\ln \frac{ m^{5} n^{3} }{ P^{2} R}\]

Answer 3

Is that the answer @peachpi ?

Answer 4

yes :)

Answer 5

@peachpi thank you you're a life saver!! :)

Answer 6

yw