SOLUTION: How do you write this expression as a single logarithm? (with a base of 3) log3(4)+2log3(x-5)-4log3(x)-3log3(x-1)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do you write this expression as a single logarithm? (with a base of 3) log3(4)+2log3(x-5)-4log3(x)-3log3(x-1)      Log On


   

Question 313525: How do you write this expression as a single logarithm? (with a base of 3)
log3(4)+2log3(x-5)-4log3(x)-3log3(x-1)
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C4%29%2B2log%283%2C%28x-5%29%29-4log%283%2Cx%29-3log%283%2C%28x-1%29%29

First, change the coefficients to powers, by the third Law of Logarithms.


Next, combine into a single logarithm, placing the factors with positive coefficients in the numerator and the negative coefficients in the denominator:
+log%283%2C%284%2A%28x-5%29%5E2%29%2F%28x%5E4%2A%28x-1%29%5E3%29+++%29

You really need to see my own website for all the FREE resources that I have there, including my OWN explanation of logarithms. To see my website, click on my tutor name "Rapaljer" anywhere in algebra.com. On my information page, click on the link to my website. Look for the link on my Homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra", then "Chapter 4 (Logarithms)". This is my OWN non-traditional explanation, complete with examples, exercises, and ALL of the answers, that my own students found much easier to understand than the regular textbooks.

See also the vidoes that are available on this topic. From my Homepage, look for the link "Rapalje Vidoes in Living Color". These are all FREE.

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