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    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 = ?
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    (Original post by Awakening)
    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 = ?
    No, because e is just a normal number, therefore the normal power rules apply
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    what's \pi+\pi^4?
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    Just as a side point, ln is not a power so you dont write ln^4, just write ln 4 or ln(4).
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    (Original post by Awakening)
    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 = ?
    As aforementioned, e is just a number (equivalent to something like 2.718; it just makes more sense to call it e than quote a long number every time.)
    So, think of something like 2^1+2^3

    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 2(1+2^2). This probably won't help you unless you are trying to cancel down a fraction.

    All you can do with e^1+e^3 is factorise e out to give e(1+e^2)
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    The log rules follow from the roles of exponentials.

    For example, e^ae^b = e^{a+b}, and so taking logs of both sides we get \ln (e^ae^b) = a+b, but a=\ln(e^a) and b=\ln(e^b), so we get \ln(e^ae^b) = \ln (e^a) + \ln (e^b). Finally, writing p=e^a, q=e^b we get the rule \boxed{ \ln (pq) = \ln p + \ln q }.

    Similarly, (e^a)^b = e^{ab}. Taking logs of both sides again we get \ln (e^a)^b = ab, but a=\ln (e^a), so \ln (e^a)^b = b\ln e^a. Finally, writing p=e^a, q=b we get the rule \boxed{ \ln (p^q) = q\ln p }.

    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").
 
 
 
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