SOLUTION: How would i rewrite this as a single logarithm? 3ln(x)+3/4ln(x+1)-ln(2x+3)

Question 240638: How would i rewrite this as a single logarithm?
3ln(x)+3/4ln(x+1)-ln(2x+3)
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
First, by laws of logarithms, the coefficients of the ln terms become exponents:

Now, the sum of ln's is a product and the difference becomes a quotient within the ln function, like this:

I have a LOT of resources on my own website on the topic of LOGARITHMS. To find my website, do a "BING" or a "GOOGLE" search for my last name "Rapalje". Near the top of the search list, you should see "Rapalje Homepage." Click on this, and look near the top of my homepage for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "College Algebra", and look in "Chapter 4"--the entire chapter is LOGARITHMS. This is my own explanation especially written for students who have trouble understanding math. I wrote this to students, NOT mathematicians, and I think you will find it MUCH easier to understand than your own traditional textbooks!! In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR.

In addition, I have a video of me teaching this topic in the classroom a few years ago.
To see this FREE video (actually there are TWO two-hour videos!), from my Homepage, look for "Rapalje Videos in Living Color". Select "College Algebra", and look for "Logarithms Part I" and "Logarithms Part II".

If you like my website, please recommend it to family and friends who have trouble understanding math!! It's ALL FREE!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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