I need sums in LOG

  • Thread starter dilan
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  • #1
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Hi,

I just need a little help in getting some sums. Can anyone of you give me a site where I can find sums in Log so that I can do them and practice a lot.

I mean like sums in this type

Show that log(xy)base16 = 1/2log(X)base4 + 1/2log(Y)base4

Thanks just need some sums of this type to practice my self.

Thanks alot people just give me a few links:smile:

Thanks
 

Answers and Replies

  • #2
arildno
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Okay, don't bother with the base change first:
Firstly:
How can you change your left-hand side from a product into a sum?
 
  • #3
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Well I mean

Ok I mean not converting to a sum. I mean to prove that you can convert it to a sum.
I mean to prove only 1 side to get the left hand side. And then show that it could be proved.

I think I expressed in the correct way because I am from a non-english country now learning in the english medium
 
  • #4
arildno
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Well, but a fundamental property about any log is that we have log(xy)=log(x)+log(y)
 
  • #5
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Ya ya I know that, but you can convert it to sums like I've shown above isn't it?
 
  • #6
arildno
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Let's take it in detail.
We have:
[tex]\log_{16}(xy)=\log_{16}(x)+\log_{16}(y)[/tex]
by the fundamental property of logs.

Now, we need to relate logs with different bases!
We have, for bases a, b, the identities:
[tex]x=a^{\log_{a}(x)}=b^{\log_{b}(x)}, a=b^{log_{b}(a)[/tex]
Thus, we get:
[tex]b^{\log_{b}(x)}=(b^{\log_{b}(a)})^{\log_{a}(x)}=b^{\log_{b}(a)\log_{a}(x)}[/tex]
Since logs are unique, we therefore have:
[tex]\log_{b}(x)=\log_{b}(a)\log_{a}(x)[/tex]
Now, let b=4, a=16, and get your result.
 

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