Question

write expression as a single natural logarithm
ln 3 - 5 ln 3

Answer 1

Need to recall some of the properties of (natural) logarithms ....
First...
\[\large p\ln \ b = \ln \ b^p\]

Answer 2

And second,
\[\large \ln \ M - \ln \ N = \ln \ \frac{M}{N} \ \ \ \ \ \ \ N\ne0\]

Answer 3

idk confuse

Answer 4

Sorry, I didn't get notified of your response :)
First, let's deal with the 5ln 3 part
Using the first property I mentioned, this is equal to
\[\large \ln \ 3^5\]right?

Answer 5

yea so would it be like L3 - 5 LN 3 3x5x3=? or is that off

Answer 6

Or no multiplication

Answer 7

No multiplication, logarithm is something different.
so let's start by gradually simplifying the expression
\[\huge \ln \ 3 - 5\ln \ 3\]
By the first property I gave you, this is equal to
\[\huge \ln \ 3 - \ln \ 3^5\]
right?

Answer 8

yea I gotcha what would be next step instead of the multiplaction like the + problems would we divide

Answer 9

or is that the final product

Answer 10

Yes, you divide. Use the second property I gave you.
(sorry if my replies are really late, I don't think I get notifications of your replies :( )