Question 553918: log2(8x) – log2(x2 – 1) = log23
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 
By the law of logarithms:
Therefore, 
Multiply both sides by x^2-1:
Subtract 8x from each side in order to set the quadratic equation equal to zero.
This one FACTORS (they usually do, don't they?):
0=(3x+1)(x-3)
There are two solutions: x=-1/3 and x=3
Since you can't have the log of a negative, you must reject the first answer. The solution is x=3.
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For this particular topic, when you find the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", choose "College Algebra" and look in "Chapter 4" for "Section 4.04 Solving Exponential and Logarithmic Equations." There is a complete explanation, illustrated with the TI84, together with lots of examples and exercises with ALL the answers given. You will especially like the "Math in Living Color" pages that go with this, where hundreds of the hardest exercises are solved for you IN COLOR! I even have TWO videos of me teaching LOGARITHMS from before I retired. Remember, it's all FREE!
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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