SOLUTION: Express as a sum, difference, and product of logarithms, without using exponents. log b square root a^7 b^6 over a^3 b^4

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Question 314541: Express as a sum, difference, and product of logarithms, without using exponents.
log b square root a^7 b^6 over a^3 b^4
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log%28b%2C%28sqrt%28%28a%5E7b%5E6%29%2F%28a%5E3b%5E4%29%29%29%29%29+
log%28b%2C%28sqrt%28a%5E4b%5E2%29%29%29
log%28b%2Ca%5E2b%29
log%28b%2Ca%5E2%29+%2Blog%28b%2Cb%29
2log%28b%2Ca%29+%2B+1

This is a VERY nice problem!!

For additional help with LOGARITHMS, please see my OWN website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on my website which is given there, and look on my Homepage for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Select "College Algebra", and look in "Chapter 4" for "4.03 Laws of Logarithms." In addition to a detailed explanation, with examples, exercises, and ALL the answers, many of the exercises are solved IN COLOR on the "Math in Living Color" pages that go with these sections.

Also, if you have trouble with LOGARITHMS, I have a video that was made a few years ago in one of my classrooms, that can be viewed from my website FREE. To see the videos look on my Homepage for the link "Rapalje Videos in Living Color." Choose "College Algebra", and look for "Logarithms Part I and Part II," probably Part II for this type of problem. Let me know if they help, or if you have questions--my Email address is at the bottom of each page of my website. Math is usually not as hard as it looks!!

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