Mechanics, Integration & Logarithms

[frog1944]

Hi,

So previously I asked the question of when to do the absolute value sign for the resultant logarithm in the integral of the type f'(x)/f(x) (https://atarnotes.com/forum/index.php?topic=170933.0), and you don't have to if the expression is always positive. But, in mechanics I rarely (if ever) see the solutions use the absolute value sign in there logarithm. Are you meant to?
Or is it determined by your own knowledge of whether the motion will always be positive?
If you use absolute value signs, can you as easily combine logarithms?

Thanks

[RuiAce]

Hi,

So previously I asked the question of when to do the absolute value sign for the resultant logarithm in the integral of the type f'(x)/f(x) (https://atarnotes.com/forum/index.php?topic=170933.0), and you don't have to if the expression is always positive. But, in mechanics I rarely (if ever) see the solutions use the absolute value sign in there logarithm. Are you meant to?
Or is it determined by your own knowledge of whether the motion will always be positive?
If you use absolute value signs, can you as easily combine logarithms?

Thanks

This.

You can almost always infer that it will be positive, and hence the absolute value signs are unnecessary.

In fact, I've never seen a situation where the absolute values could be necessary at all.