SOLUTION: rewrite the expression as a single logarithm 3*ln(x)+2*ln(y)-(1/3)ln(z)

SOLUTION: rewrite the expression as a single logarithm 3ln(x)+2ln(y)-(1/3)ln(z)

Question 328678: rewrite the expression as a single logarithm
3*ln(x)+2*ln(y)-(1/3)ln(z)
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
3 log x + 2 log y-1/3 log z

First, by the third law of logarithms, the coefficients become exponents like this:

Now by the first and second laws of logarithms, this can be written:

Now it just so happens that LOGARITHMS from College Algebra, like FACTORING in all of my algebra classes,is one of my FAVORITE topics! I have a COMPLETE explanation of this topic, in my own curriculum that I'm giving away FREE on my own website! To see this website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on my website name that you will see there, and look on my Homepage for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra" and look in "Chapter 4" for the entire chapter. These are my own explanations that are written especially for students who have trouble with math!

In addition, many of my exercises are solved in my "Math in Living Color" pages that accompany each of these sections.

Not only do I have a complete written explanation for this topic, I also have TWO videos that were made a few years before I retired. The videos are also FREE, and you can see the videos by looking on my Homepage for "Rapalje Videos in Living Color." From here, choose "College Algebra" and look for the videos on Logarithms Part I and Part II. You may need to download RealPlayer, if you do not have it already on your computer, but this too is a free download. And, you don't have to watch the whole video, but I have indicated on the video pages where to look for each particular type of logarithms problem.

I hope you like my curriculum and my videos. I have other topics as well. When I was teaching, my own students were unanimous that my explanations were a LOT easier to understand than the traditional textbooks. If you like it, please recommend it to your family and friends who need help with math!! Like algebra.com, it's all FREE!!

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