# Thread: Logarithms and Logarithmic Functions

1. ## Logarithms and Logarithmic Functions

Just found this site and looks like it can be very helpful. I'm not asking for my homework to be done, I just have a few example problems I need help with, then I can figure it out on my own. I'm in an independant study type class where I learn the material on my own, and just take the test for each chapter to pass the class. Here are some problems I can use some help with:

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Problem 1
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log3 y = 1/2 log3 81

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Problem 2
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log6 (x+1) - log6 (x-1) = log6 9

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Problem 3
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log4 n = 2 log4 8

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Problem 4
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Use log4 7 = 1.4037 and log4 3 = 0.7925 to evaluate log 7/3

Example: log4 = log (subscript) 4

Thanks! I appreciate any help given!

2. Originally Posted by toop
Just found this site and looks like it can be very helpful. I'm not asking for my homework to be done, I just have a few example problems I need help with, then I can figure it out on my own. I'm in an independant study type class where I learn the material on my own, and just take the test for each chapter to pass the class. Here are some problems I can use some help with:

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Problem 1
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log3 y = 1/2 log3 81
i will use the following notation: log[a]b means log to the base a of b

log[3]y = (1/2)log[3]81
=> log[3]y = log[3]81^(1/2) ...........since nlogx = log(x^n)
=> log[3]y = log[3]9
=> y = 9

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Problem 2
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log6 (x+1) - log6 (x-1) = log6 9
log[6](x + 1) - log[6] (x - 1) = log[6]9
=> log[6]{(x + 1)/(x - 1)} = log[6]9 ............since logx - logy = log(x/y)
=> (x + 1)/(x - 1) = 9
=> x + 1 = 9x - 9
=> 8x = 10
=> x = 5/4

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Problem 3
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log4 n = 2 log4 8
log[4]n = 2log[4]8
=> log[4]n = log[4]8^2 ..............since nlogx = log(x^n)
=> log[4]n = log[4]64
=> n = 64

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Problem 4
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Use log4 7 = 1.4037 and log4 3 = 0.7925 to evaluate log 7/3

is it to evaluate log[4] (7/3)? or is it log[10]?

3. Oops sorry, yes it is to log[4] (7/3)

...And thank you VERY much for the help on the other problems. Helped me tremendously.

4. Originally Posted by toop
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Problem 4
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Use log4 7 = 1.4037 and log4 3 = 0.7925 to evaluate log 7/3

log[4](7/3) = log[4]7 - log[4]3 ...................since log(x/y) = logx - logy
................= 1.4037 - 0.7925
................= 0.6112