We know that (ln^4) + (ln^1) = ln^4 because of the log rules,
however, how do you add e's - are there any rules?
e.g e^1 + e^3 = ?
How to add e's Watch
- Thread Starter
- 19-12-2010 17:07
- 19-12-2010 17:10
- 19-12-2010 17:12
- 19-12-2010 17:14
Just as a side point, ln is not a power so you dont write ln^4, just write ln 4 or ln(4).
- 19-12-2010 17:37
So, think of something like
You'll be using indice rules for this - which only really apply to the multiplication/division of numbers. If you think back to indices, you'll probably remember that when you add/subtract them, there's nothing you can do.
The only thing you can really do is factorise a bit to give you . This probably won't help you unless you are trying to cancel down a fraction.
All you can do with is factorise e out to give
- 19-12-2010 18:49
The log rules follow from the roles of exponentials.
For example, , and so taking logs of both sides we get , but and , so we get . Finally, writing we get the rule .
Similarly, . Taking logs of both sides again we get , but , so . Finally, writing we get the rule .
In other words, addition of logarithms corresponds to multiplication of exponentials, and multiplication of logarithms corresponds to exponentiation of exponentials. There's no such corresponding result for the addition of exponentials, and hence no such rule (other than "just add them").Last edited by nuodai; 19-12-2010 at 18:50.