Question 224294: I need to solve ln(x)= 3-ln(x+2)
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! ln(x)=3-ln(x+2)
The first step is to get all the logs on one side, in this case by adding ln(x+2) to each side:
ln(x) + ln(x+2) = 3
By the law of logarithms,
ln(x(x+2))= 3
ln(x^2 + 2x) = 3
Next "undo" the ln by raising both sides as a power of e:
x^2 + 2x = e^3
The best way to solve this is by completing the square:
x^2 + 2x + 1 = e^3 + 1
(x+1)^2 = e^3 + 1
Take the square root of both sides:
Subtract 1 from each side:
Both answers appear to be acceptable, since if you plug them in to the original equation, they do NOT result in a log of a negative.
If you need additional help with Logarithms, I hope you will check out my own website. I have a LOT of help for you there. To find my website, do a "Bing" Search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. Then, near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time," select "College Algebra" and in Chapter 4, you will find an entire chapter on Logarithms. This is my own non-traditional explanation that my own students have found MUCH easier to understand than the traditional textbooks. In addition to my explanations, examples and exercises, I have my "MATH IN LIVING COLOR" pages where I solved many of these exercises IN COLOR!!
There are TWO 2-hour videos filmed in my own classes a few years ago that can be viewed FREE from my website. To see these videos, from my Homepage, look for "Rapalje Videos in Living Color". Select College Algebra, and look for Logarithms Part I and Logarithms Part II. I must apologize that the videos are a few years old, and my calculator explanation is VERY out of date!!
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamone Springs Campus
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