Question 219288: log69 + log64
the two 6's are subcript
Can you please write this expression as a single logarithm and simplify it? Please do it in steps because I just started this and do not understand.
Thank you!
Found 3 solutions by user_dude2008, stanbon, rapaljer:
Answer by user_dude2008(1862)   (Show Source):
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! log69 + log64
the two 6's are subcript
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log(base6)9 + log(base6)4
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= log(base6)[9*4]
= log(base6)36
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This last line says you want the
exponent of 6 that gives you 36.
The answer is 2
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= 2
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Cheers,
Stan H.
Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! 
The basic Law of Logarithms that applies here is "when you add logarithms that have the same base number, you MULTIPLY!" Actually, this is the reverse of the Law of Logarithms that says "when you MULTIPLY, you ADD the logarithms."
Now,  means "what POWER would you raise 6 to in order to get 36?" Of course, the answer is 2.
You may want to see my detailed explanation of LOGARITHMS on my website. If you do a "Bing" search for my last name "Rapalje", look for "Rapalje Homepage" near the top of the search list. Click on this, and look for the link near the top of the page "Basic, Intermediate, and College Algebra: One Step at a Time." Select "College Algebra", then look in Chapter 4 for my topics on Logarithms. This is my own NON-traditional explanation presented in a way that you will find is easier to understand than your own textbooks. It is supported by "MATH IN LIVING COLOR" pages, and also two two-hour videos of me teaching the topic of Logarithms (all free--I have nothing to sell you!).
To see the videos, return to my Homepage and look for the topic "Rapalje Videos", followed of course by "College Algebra."
Please let me know if this helps you!!
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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