SOLUTION: log6(x-3)+log6(x-4)=-2

Question 308648: log6(x-3)+log6(x-4)=-2
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

By the Laws of Logarithms (see my website mentioned below for additional explanation!):

By the definition of logarithms, this means

Now, it gets REALLY ugly! You can either set it equal to zero and solve by the quadratic formula (it doesn't factor!), or you can complete the square. I will try the latter.

What does on the blank line above is "half of -7, then squared".

The answer for x must NOT make ANY of the logarithms NEGATIVE. If it does, it must be rejected!! Therefore the answer must be GREATER THAN 4. It seems that the answer is just BARELY greater than 4, so it is acceptable. The other answer is not, so it must be rejected.

I have to admit, that MY problems do NOT come out this way. I hope I've done it correctly. If I have an ERROR here, someone please tell me, so I can correct it. If you want some easier problems with some EASIER explanations, please see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then click on my website. On my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Then choose "College Algebra", then "Chapter 4 (Logarithms)", and see Section 4.04. I have a complete explanation of Logarithms that I think you will find my explanation a lot easier to understand than traditional textbooks. Besides this, many of my exercises are solved IN COLOR in the MATH IN LIVING COLOR pages that go with this.

In addition to my written explanations of this topic, there is a video explanation from my own classes from before I retired. All of this is FREE if you have RealPlayer. If you don't have RealPlayer, then it is a FREE download.

I have many other topics from Basic, Intermediate, and College Algebra that are explained in detail, with many of these topics explained on video as well. Everything on the website is FREE.

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

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