Question

Write the expression as a single natural logarithm.

3 ln x - 2 ln c

Answer 1

Use this rule twice:

\(a\cdot log(b) = log\left(b^{a}\right)\)

Answer 2

Whats the value of a and B?

Answer 3

This is where you look at your problem statement and try to draw parallels with the example and rule. This answers your question directly.

Answer 4

and then use this rule

\[\log p -\log q = \log(p/q)\]

Answer 5

I still don't get where im suppose to plug in the numbers

Answer 6

\(a*\ln(x) = \ln(x^a)\).
Therefore,
\(3*\ln(x) = \ln(x^3)\)
\(2*\ln(c) = ?\)

Answer 7

ln(x^2)?

Answer 8

In the second part of the original problem, is it x or c?

Answer 9

oh its 2*ln(c)=ln(c^2) ?

Answer 10

okay. Subtract the two parts. Use the formula given by UnkleRhaukus to simplify.

Answer 11

\( \Large 3*\ln x - 2*\ln c = \ln(x^3) - \ln(c^2) = \ln(\frac{x^3}{c^2})\)

Answer 12

I was gonna do it! lol haha cx But ok thanks :)

Answer 13

You are welcome.