dimension !
What do you mean by "don't have dimension"?
They are just mathematical functions. The units of x are what matters.
They are just mathematical functions. The units of x are what matters.
closed account (S6k9GNh0)
ln(x) is equal to log base e of x. I don't remember what exp is if anyone cares to reminisce.
I think I know what he means.
majidkamali1370, have you done any integral calculus? If so, you might know that the power rule has an exception for ∫x-1dx. Integrate that and you get ln|x|. ln|x| is dimensionally one step up from 1/x, which puts it in a position of no dimension (that was a terrible explanation, anyone care to help me out here? It's late at night and I haven't had coffee all day).
As for exponentials, those are a completely different ballgame. Multiplication can be thought of as a way of writing out a long chain of additions in parenthesis in a smaller space, while exponents can be thought of as a way of writing out a long chain of multiplications in a smaller space. An exponential's base is a constant, which may or may not have units associated. If it has none, then no matter how many times you multiply that constant by itself, you'll get no further units (does this make sense?). If there are units associated, then you do get more units in your formula.
...that was a terrible explanation, but I think you understood?
-Albatross
majidkamali1370, have you done any integral calculus? If so, you might know that the power rule has an exception for ∫x-1dx. Integrate that and you get ln|x|. ln|x| is dimensionally one step up from 1/x, which puts it in a position of no dimension (that was a terrible explanation, anyone care to help me out here? It's late at night and I haven't had coffee all day).
As for exponentials, those are a completely different ballgame. Multiplication can be thought of as a way of writing out a long chain of additions in parenthesis in a smaller space, while exponents can be thought of as a way of writing out a long chain of multiplications in a smaller space. An exponential's base is a constant, which may or may not have units associated. If it has none, then no matter how many times you multiply that constant by itself, you'll get no further units (does this make sense?). If there are units associated, then you do get more units in your formula.
...that was a terrible explanation, but I think you understood?
-Albatross
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No. I mean for example in ' a = F ^ 2 ' unit of a is newton^2 (for example).
but in ' b = ln (x) ' , b has no dimension or we need to ply a constant to create
unit for b like this ' b = c * ln (x) ' . if unit of ' c ' is newton/meter , unit of b become newton/meter and ln(x) (and exp too) has no dimension. why?
but in ' b = ln (x) ' , b has no dimension or we need to ply a constant to create
unit for b like this ' b = c * ln (x) ' . if unit of ' c ' is newton/meter , unit of b become newton/meter and ln(x) (and exp too) has no dimension. why?
Actually it's really not that simple. How many of you have taken Electricity and Magnetism?
-Albatross
-Albatross
If I am understanding you (no guarantee) then the formulae don't have units because those are for you to supply.
When you say 3m (meaning 3 metres) you are saying scalar '3' x unit 'm'. Or 3 lots of one meter units.
Raw functions like ln(x) can be applied to any units you want. You decide. There is nothing mathematically special about m (meter). Its just a place holder for the mathematician to keep track of that quantity (one meter lengths).
When you say 3m (meaning 3 metres) you are saying scalar '3' x unit 'm'. Or 3 lots of one meter units.
Raw functions like ln(x) can be applied to any units you want. You decide. There is nothing mathematically special about m (meter). Its just a place holder for the mathematician to keep track of that quantity (one meter lengths).
Here's my guess:
lets say we have two variables A and B
then lets say that C = A - B
now, I assume, that this means, that the units of A, B and C are the same
lets say, that A = ln(x), where x is in meters and B = ln(y), where y is also in meters
now C = A - B = ln(x) - ln(y) = ln(x/y)
x/y has no units so C couldn't have any either
due to my assumption neither does A or B
lets say we have two variables A and B
then lets say that C = A - B
now, I assume, that this means, that the units of A, B and C are the same
lets say, that A = ln(x), where x is in meters and B = ln(y), where y is also in meters
now C = A - B = ln(x) - ln(y) = ln(x/y)
x/y has no units so C couldn't have any either
due to my assumption neither does A or B
Well, then C would be ln(square meter). That doesn't give of any information though. It's just going back to where we started. Now the question is what are the units of ln(square meter).
If you put meters in, you get meters out.
If a ball travels 2 meter in 3 second then what are the units of speed?
2 meters every 3 second is 2 meters per 3 seconds.
speed = 2 meters / 3 seconds, or 2/3 x m/s
So the unit of speed is m/s and there are 2/3 of them.
You put meters and seconds in you got meters and seconds out, along with their relationship to one another.
If a ball travels 2 meter in 3 second then what are the units of speed?
2 meters every 3 second is 2 meters per 3 seconds.
speed = 2 meters / 3 seconds, or 2/3 x m/s
So the unit of speed is m/s and there are 2/3 of them.
You put meters and seconds in you got meters and seconds out, along with their relationship to one another.
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| If you put meters in, you get meters out. |
Here's some stuff for you lot to chew on.
http://www.sciforums.com/showpost.php?p=1331961&postcount=11
EDIT: hamsterman liked an explanation of mine... <3
-Albatross
http://www.sciforums.com/showpost.php?p=1331961&postcount=11
EDIT: hamsterman liked an explanation of mine... <3
-Albatross
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