Question 237321: Expand: Log2{x^4y^3/5n^2}
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 
The log of a quotient is the DIFFERENCE of the logs:
Now, the log of a product is the SUM of the logs:
Finally, "bring down" the exponents:
OOPS! One more step! Use the distributive property to remove those last parentheses:
It just so happens that I have quite a few resources on the topic of LOGARITHMS, including my own "non-traditional" explanation both in written form and in video form that can be obtained free from this website! Do a "Bing" or "Google" search for my last name "Rapalje". Near the top of the search list, look for "Rapalje Homepage." Near the top of my Homepage, look for the link "Basic, Intermediate and College Algebra: One Step at a Time." Select "College Algebra" and look for "Chapter 4 Logarithms". This specific question is explained in detail in my "Section 4.03 Laws of Logarithms." See also the "MATH IN LIVING COLOR" sections that correspond to these sections, where many of the exercises I have provided are solved in great detail, even better IN COLOR!!
I also have some videos from my own classroom teaching (a few years ago!). To see the videos (did I mention FREE videos???), from my Homepage (near the top!), look for "Rapalje Videos in Living Color". Choose "College Algebra", and look for "Logarithms Part I" and "Logarithms Part II."
I LOVE TO HELP with logarithms, so send me your questions by Email. I'll answer as time permits!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
If you need more help on this topic of the distributive property, please see my own website for my "non-traditional" explanation. Do a "Bing" or "Google" search for my last name "Rapalje". Near the top of the search list, look for "Rapalje Homepage." Near the top of my Homepage, look for the link "Basic, Intermediate and College Algebra: One Step at a Time." Select "Basic Algebra" and look in Chapter 1 for "Section 1.06, Combining Like Terms and the Distributive Property". Other sections here may also be helpful.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
|
|
