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1. getting confused about basic logarithm principles
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2. Re: getting confused about basic logarithm principles
Firstly, is the same as , just like is the same as .

Now the log law that you're getting confused by is:

For the numbers we are interesting in, the log law becomes:

You are claiming that we can use this law to imply that . But looking at the above law, you would need on the left-hand-side for it to work.

So maybe your confusion stems from your belief that . This is not true.

For the left-hand-side, you take the logarithm of and you square the answer. For the right-hand side, you find the logarithm of . Two different things are happening here so you cannot say that both sides are equal.

What you are saying (I'm still asssuming this) is similar to believing that e.g. is the same as .

Does that make sense? Let me know if it's something else which you are confused by.
Last edited by notnek; 07-05-2012 at 05:58.
3. Re: getting confused about basic logarithm principles
(was too slow, but I'll post this anyway)

and mean different things - with one you take the log then square it, with the other you square first then take the log.

The relevant logarithm rule here is: . Because isn't necessarily the same as then it's not correct to say .

With regards to your other question, . They both represent taking the log of x, then multiplying by 2. The brackets just add clarity.

One type of notation you should avoid using, however, is . Here it's not obvious whether you take the log or square first. You need brackets to clarify that.
4. Re: getting confused about basic logarithm principles
(Original post by notnek)
Firstly, is the same as , just like is the same as .

Now the log law that you're getting confused by is:

For the numbers we are interesting in, the log law becomes:

You are claiming that we can use this law to imply that . But looking at the above law, you would need on the left-hand-side for it to work.

So maybe your confusion stems from your belief that . This is not true.

For the left-hand-side, you take the logarithm of and you square the answer. For the right-hand side, you find the logarithm of . Two different things are happening here so you cannot say that both sides are equal.

What you are saying (I'm still asssuming this) is similar to believing that e.g. is the same as .

Does that make sense? Let me know if it's something else which you are confused by.
thanks! all that made sense ..so can log(x)2 be written as something else, like in the way that log(x2) = 2 log x
5. Re: getting confused about basic logarithm principles
(Original post by CasualSoul)
thanks! all that made sense ..so can log(x)2 be written as something else, like in the way that log(x2) = 2 log x
No. I forgot to mention this in my previous post:

There is no log law which can simplify two logs with a multiplication between them. So the most simple way of writing is .
6. Re: getting confused about basic logarithm principles
(Original post by CasualSoul)
thanks! all that made sense ..so can log(x)2 be written as something else, like in the way that log(x2) = 2 log x
Also, watch out with how you've put the brackets when writing log(x)2 as it's not obvious whether the squaring or the log comes first.
7. Re: getting confused about basic logarithm principles
(Original post by ttoby)
Also, watch out with how you've put the brackets when writing log(x)2 as it's not obvious whether the squaring or the log comes first.
ohh right so should I include double brackets for the bit that comes first?

Edit ^ ignore that ..so would (log(x))^2 mean that you do log x and then square the answer?
Last edited by CasualSoul; 07-05-2012 at 06:10.
8. Re: getting confused about basic logarithm principles
(Original post by CasualSoul)
ohh right so should I include double brackets for the bit that comes first?

Edit ^ ignore that ..so would (log(x))^2 mean that you do log x and then square the answer?
Yes, that's what it means.
9. Re: getting confused about basic logarithm principles
(Original post by CasualSoul)
ohh right so should I include double brackets for the bit that comes first?

Edit ^ ignore that ..so would (log(x))^2 mean that you do log x and then square the answer?
Yes, that's what it means. The way I've been writing it is also fine

If you are typing it on a keyboard without LaTeX (the formatting you see above) then it's probably best to write it as (log(x))^2, as you've done.
10. Re: getting confused about basic logarithm principles
Cheers!